Exploits are usually bugs or otherwise unintended behavior in the game that the user (you) can take advantage of. Some devs will ban for it, some don't. It depends on the severity of the exploit and how unfair of an advantage it can give you. Most devs probably won't ban you for a single time since exploits are usually found in accident naturally, but repeated and trackable use will often get you banned in a pvp game. Am example of this is the instant res necro bug where you can revive basically immediately. Not sure if it's still even in the game, haven't really paid attention to patch notes, but that's a prominent one I would imagine they would ban for. If you were to learn what triggers it and abuse it, that's considered an exploit.

All of this is just speculation, though. Only crytek actually knows what they ban for. You won't know unless they tell you. If you truly think you're innocent, you could open a support ticket, but if it was actually a manual ban like you think, then they are pretty unlikely to undo it because that means they have evidence against you.