Gameplay programmers are responsible of the "game" part of the software. What this means is that they're usually responsible, depending on the type of game, for the 3Cs:
- Character - the playable character
- Camera - how the player sees the world
- Controls - how the player interacts with the world
These tasks include a lot of dependencies with the engine, such as playing animations, reacting to collision, making sure the actions are replicated properly over the network, etc...
The creation of mission items for level designers / mission scripters is also often done by the gameplay programmers.
Some teams will have AI programmers, but if it's not the case, gameplay programmers do the AI as well, which includes behaviors, navigation, player feedback, etc...
It's a pretty broad field and depends a lot on the game type you're working on.
Gameplay is often programmed in the "native language" of the engine, but can also be scripted using a higher level language, such as Lua, Python, Unreal Script, etc...