Undermounted sinks are fitted below the worktop, with a polished hole cut in the stone forming the “entry” to your sink. Tapholes must be cut into the stone, and many people also have drainage grooves ground and polished into the top surface.
Topmounted sinks sit on top of the worktop, with a flange or lip sealed down onto the stone. Because the hole through the stone is not visible, it doesn’t need to be polished. Tapholes are normally in the “tray” of the sink itself and do not need separate cuts in the stone. the drainage area is integral to the sink and cannot be cut into the stone.
More definitions (including of other sink types) can be seen in our glossary, here.
A regular question we here is which of these two basic types is better. There is no one right answer; issues of taste and lifestyle will make customers lean more one way or another.