Function generator output
how does the current behave? 


It flows in a loop from a to b to c to d back to a.


  If d is grounded, doesn't current just leave the loop?


By Kirchhoff's Current Law, for every current flowing in to ground (assuming the ground symbol means a connection to some large conductive body) there needs to be another current flowing out of ground. But since there's only one connection from your circuit to ground, there can't be any return flow, and therefore the current flowing into ground is zero.

Really, the ground symbol here doesn't represent a connection to something outside the circuit. It just tells you what node will be used as a reference to define the voltage at the other nodes.


  What does the voltage output actually mean?


That needs to be provided as part of the problem definition. 

It could be the voltage at a or b or c or d. 

Only one of those choices will make the problem interesting, but in general, a circuit problem statement should make clear what terminal is considered the output of that circuit.