Can current flow in one circuit complete another circuit?
If C2 is a DC circuit, and both C1 and C2 share a common ground, putting a N channel MOSFET at the ground of C2 and driving the gate from C1 is a common setup.  Drain of the MOSFET is connected to where C2 used to be grounded.  Then the Source of the MOSFET is connected to ground.  When the Gate of the MOSFET is driven high enough, the junction turns on an C2 is grounded and power flows.  

Make sure the current and voltage capability of the MOSFET is greater than the demands of the C2 circuit, as well as turn on gate voltage low enough to be driven by C1.  MOSFETs that can be driven by lower voltage circuits are commonly called "logic level" MOSFETs.

As Leon said in the comments, a relay is a easy way to drive something that is AC or much higher power without getting yourself into trouble.  Sometimes with very low powered circuits, you will need a MOSFET to drive the relay.  Just make sure to look at how diodes are put on coils of relays to short out the voltage spike generated when power is removed from the coil.