Ok lets take a step back and look at what NO aim acceleration is. Having no acceleration is what we call 1:1 controls. 1:1 controls basically means one unit of movement in your mouse or joystick equates to one unit of movement on the screen. It's linear, like this:
This is your optimal state. It's nice, clean, and consistent. 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. The very worst examples of this in the industry are Halo 5 and Rainbow Six Siege (console version). They don't only have aim acceleration, but they have acceleration jumps, which means it's not even a curve like you see above...its a wavy line. You'll also find really bad aim acceleration in games like Skyrim. It's an archaic concept and should have been killed off when games like COD and BF showed us how it should be.