I advise you guys don't get caught up in the terminology, as it's pretty much 100% arbitrary. when i use the word "heavy offense" or "hyper offense" or even "offense" these all mean the same thing to me, that I'm trying to kill the other guy before he kills me. that's the bottom line. pretty much everything ssbbm said I agree with and it is extremely informative, but it might be a tad specific.
here are 2 concepts that I think go into having a good pokemon team:
1. make the opponent respond to you. this goes back to Surgo's original D/P threat list, where he made a disclaimer that you should always be trying to make the opponent respond. He said that in gen IV, there were simply too many different threats to play a reactive play style consistently, hence the better idea is to pose the threat than react. in gen V, there are even more threats and the only really notable defensive pokemon gained were burungeru and ferrothorn, off the top of my head.
NOTE: this does not mean stall is bad, but rather that the good stall is going to be the aggressive kind that gets its hazards up quickly and eliminates wall breakers quickly. in other words, the kind that doesn't just sit around waiting to get smashed. if you look at the greats, most notably IPL in my eyes, you'll see that this is an underlying theme.
2. have a unified purpose that every member of the team contributes to. this is a concept that is true of most real-time strategy games, with the easiest parallel to draw being various tcg decks. you don't just throw a bunch of strong cards together: they must work towards a purpose. similarly in pokemon, you will do much better if your pokemon help each other in some way. they don't necessarily have to lead to one pokemon's sweep or anything like that, but they should help each other out. i.e. if you have dual screen deoxys as a lead, you should have lots of pokemon that like not taking much damage for a few turns. conversely, if you have dual hazards deoxys, you should have lots of pokemon that hit hard on things that stay in, forcing the opponent to switch a lot and take maximum extra damage. little things like this cause your team to work better as a unit.
additionally, if you fulfill #2, you are far more likely to fulfill #1 because your opponent is forced to try and respond to your play unless they let you carry it out without a hitch, in which case you should win.
3. don't 100% rely on only one way to win. if your team makes life perfect for cm rest sleep talk suicune, but can't win without him, and your opponent just happens to carry raikou, celebi, roar vaporeon, explosion heatran, and other things that make his life difficult, then you are going to lose. thus, your team should be able to win in multiple ways, not just one. in the above example for instance, if heatran exploded on your suicune, that might be okay if you can toxic spikes them to death. toxic spikes also help suicune a lot by stalling stuff. oh hey, suddenly you're not lost without suicune.
these concepts are I think pretty basic and apply to all pokemon teams, not just offense. keep in mind, there are no hard and fast rules. if you blindly follow rules, you only limit your own creativity. thus, I encourage you guys to question every "rule" that I or anyone else tells you about pokemon.
anyways, how does this all apply to offense? well, I think ssbbm covers a lot of that, but remember, you should never blindly follow rules but always be questioning them. anyways, I'll give a little summary of how I think the above concepts apply to offense.
1. make the opponent respond to you. well, I think this is where a lot of the controversial things I say come from. like, I don't like choice scarfs, because they lock you into a move without very much power attached to it. this means your opponent can very easily come in and take advantage of you with a resist or bulky pokemon, forcing you to switch around and be on the back foot. basically, I think the less you have to switch, the better, because switching takes a turn where you could be doing something towards winning and spends it changing pokemon instead. obviously, you have to switch, so you shouldn't just stay in all the time, but if you make your team so that you don't have to switch as much, you can spend more of your turns smashing things with strong attacks that your opponent has to respond to.
the easiest way to not have to switch is to use pokemon that set up. by nature, they don't like switching. they can switch moves, and usually because of boosts they are very powerful and don't give away many free turns. of course, there are other ways as well. I'm sure you guys all know how specs tornadobro works. flying is barely resisted by anything, so shooting off a huge attack that isn't resisted by much coming off of fast speed, you don't have to switch much. you can just spam hurricane. that's just one example. strong u-turners fit the bill too. I mean, if you hit an opponent with a cb u-turn from scizor, you are switching but you are still using a strong attack, and if they switched that means you can go to a pokemon that beats them. you haven't wasted any time, and you are still forcing the opponent to respond to you. that's the bottom line. keep the opponent on the back foot and you will win.
2. have a unified purpose. I think this one is pretty easy for offense, since the purpose is always "kill the opponent fast." to do this, you have to do things like kill walls and kill revenge killers. this is where the "all physical" or "all special" concept comes from. if you use a bunch of special sweepers, and your opponent's team is a bunch of physically bulky pokemon and blissey, then once you kill blissey you are hitting the rest of the opponent's pokemon on their weaker defense stat, helping you kill them faster. thus, all of your pokemon suddenly become really dangerous to that team, because only blissey can handle them. that means no one pokemon is supremely valuable to your team in this battle, because you can do huge damage with all of them. thus, if you sacrifice two guys to do, say, 60% to blissey, and then force her out and take more sr/spikes damage when she comes back in, she can't handle the next guy. so, even though you've lost 2 pokemon to only do a little more than half to one pokemon, suddenly you are at the advantage because blissey can no longer handle the rest of the team, and the rest of the team is short pickings afterwards. if you use lots of different types of attackers, then your opponent is more likely to have an answer to every pokemon you have, meaning you have to kill lots of pokemon before you can win, rather than just one or two.
this doesn't mean that you have to go all physical/all special though. if you have a bunch of pokemon that are very difficult to counter outside one or two answers that counter them all, then you slap those all on a team. let's say, in gen IV, you have dd gyarados, agility empoleon, life orb heatran, dd salamence, and other pokemon that are all countered by defensive water types. your opponent might carry two at most. once you overpower them by sacrificing your guys to do damage, you will make short work. note that this hypothetical team has 2-3 physical and 2-3 special sweepers (disclaimer: this is all off the top of my head so if the team sucks/is incomplete, don't judge me, it's just for an example).
3. don't rely on one way to win. this is also easy for offense, since almost every pokemon you use will be able to do a lot of damage quickly and thus win games. a nice rule of thumb that I like is once you have your team of 6 pokemon, take out one pokemon and turn it into a team of 5 pokemon. could it still work decently well in a hypothetical 5v5 metagame? do this with every pokemon, and if you can answer yes for every guy on the team, then you know you are really not relying on anyone. that should also show you that sometimes, if called for, it's ok to sacrifice a guy for the good of the team, even if he's not "death fodder" (i.e. weakened and useless).
again, that's not a rule by any stretch of the imagination, and a team is not necessarily bad if it can't do without a pokemon. it's just a little exercise I like to do.
If you apply these concepts to offense, you get a type of offense that doesn't switch much and tries to force the opponent to react, as opposed to the kind that facilitates maneuvering around the opponent with revenge killers and defensive pokemon. this is a good type of offense too, just different. to differentiate the two, I used to call the former "heavy offense," referring to the idea that it skips the bells and whistles and focuses more heavily on hurting things. some of my friends called it "hyper offense," with the same idea in mind. we shortened it to "HO" because that's easier to type fast. the bottom line is there is no official terminology. at the end of the day it's all just offense. this take on it has been around long before me as well, so I'm not trying to take credit for naming it or whatever.
anyways, if you apply these concepts, this sometimes means lots of setup sweepers since they switch less. if you have enough, dual screens fit well. thus, the concept of "dual screens + 5 sweepers." I wouldn't say that type of team is the definition of "heavy offense," just an example.
sorry for the length of the post. I could probably make it more concise or format it and make it pretty but I can't be assed right now. thanks for reading.