Ok to understand ballistic curves, you need to start with what 1:1 controls are.
1:1 controls basically means one unit of movement in your mouse equates to one unit of movement on the screen. It's linear, like this:

This is your optimal state. Everything else is unpredictable. This is what all games should strive for, however...
A lot of the time, game controls aren't linear. Developers, trying to be too clever, will implement all sorts of crazy ideas. The most common is aim acceleration, which means the further you hold left for example, the faster the cursor goes. So pegging the stick half way may equate to one unit in cursor movement, HOWEVER peg it all the way (double the distance in stick movement) may equate to three units in cursor movement (instead of two). Basically - your cursor moves faster depending on how far you peg the stick.
So it ends up looking like this:

This originated from the early days of console when no one was used to playing with dual analogue controls, so they were trying to find all sorts of unique solutions to help ease people into them. Those days are over, yet developers still cling onto these old concepts for some weird reason, even though industry leading games like BF and COD have largely moved away from them.
So what the XIM developers need to do is basically turn the second graph into the first. To do this, they create a counter-curve, which we call a Smart Translator. Think of this as a sort of default ballistic curve. But when gamers talk about "ballistic curves", they are not referring to this default one. Read on...
Now after all this, 99% of people are happy, however some gamers still want to modify it. Generally they like to do things like re-introduce aim acceleration, or fight off the effect of aim assist. To do this, they create a custom curve which which we call a "ballistic curve", which sits on top of the standard 1:1 Smart Translator.
In essence:
1) XIM devs bring the curve from diagram 2 to 1 by using a "Smart Translator" (which you can think of as the default ballistic curve).
2) Gamers then bring the curve from diagram 1 back to 2* by using a "Ballistic Curve".
*this is not 100% accurate but it gives you a rough idea of what's going on here.As a general recommendation, don't create your own ballistic curve until you find yourself in need of one. Just because it's found in the "Advanced" area, don't make the mistake of equating Advanced with Better. A lot of very experienced XIM'ers here on this forum just use vanilla ST's for 99% of their games.