Sorry Arcticblast, I couldn't help myself. :s
Anyway, here goes:
To me,
Pokemon and battling is like a language. This may sound very bizarre to most people, but hear me out.
While nowadays I'm less known, back in the BW and early XY era I got many opportunities to perform in top level play (including one SPL; the first to feature Doubles OU as a format). After these experiences, I really dropped off the radar due to the pressure I personally felt to keep winning; as in my mind not doing so meant I wasn't representing my community and was letting it down. I eventually just had to leave due to how hard it was for me to keep going with this twisted mindset. Only recently have I come back, and to tell the truth its still tough to handle the pressure sometimes.
While on my hiatus (if that's what you want to call it), I needed a different mindset, one I got from a friend of mine who happened to play VGC. We started hanging out a lot and I personally was really happy to see someone who just enjoyed playing the game. The competitive spirit was definitely still there mind you, but at the same time we loved sharing ideas and reasoning as to why we did what we did. It really started to grow on me that the logic and decision-making were simply a way of communicating and interacting. At the end of the day, the decisions we make help to define who we are as pokemon trainers. None of us is truly the same, we all think and feel differently about different ideas and topics. And if I took anything away from this, its that this uniqueness is something to be respected and appreciated.
In this way I find battling very similar to speaking a language. It's not something that comes naturally (though I am sure many of us have a talent for many aspects of battling), it is something you learn and master over time, with practice. Additionally, we don't all speak it the same way, similar to how many languages have different sub-accents and phrases in different areas. And most importantly, it is definitely a way we express ourselves and our thoughts to each-other. This is a very broad way of looking at it, so maybe this all just flew past you, but this is the mindset I myself have adopted. It really helps me to not feel quite as pressured when pressed with a challenge, and really just savor the moment.
Now, when we take a look into the whole "dance" concept that
Hashtag provided, looking at it with the "language" comparison makes a bit more sense (to me at least). What we are really doing at those higher levels of play is having this kind of "conversation" with each-other. The opponent obviously isn't just telling you something extreme, like "imma switch out now", but each turn that goes by they are communicating their mindset to you, and this by extension can help you gain a sense of what their next move may be. Now if you want to call it "prediction" or whatever, but in all honesty it's much more like an inference. At the same time, you know the opponent is also making observations and inferences, and this leads to the aspect
Lohgock was describing. Inferences, while based on fact, are not truly fact themselves, leading one to want to avoid them when and wherever possible in favor of a more reliable play that covers more options in exchange for less of a reward. The issue here is that you need an advantage over the opponent before making these sorts of trade-offs would lead to a winning situation for you. In this sense its about scouting out what your opponent is doing to try and gain information, and from here you will usually use this information to get a sense of how the opposition is playing. At whatever point you feel like you have that sort of intuitive grasp on an opponent's mindset, you will start making those inferences. From there it's about getting a good enough advantage so that those safe and reliable plays can grind you out to a win.
At the end of the day though, everyone views and plays the game differently. And I think that is what makes "what is battling to you?" such a hard question to answer, as it really means something different to every individual.