I am confused with the idea of a current sink/current mirror circuit. Why not just have the current sink to ground? Can anyone explain this to me? Thanks.
A current sink is not a circuit, it is a circuit function. For example an NPN transistor with the emitter connected to ground will sink current to ground when turned on.
A current mirror normally consists of two transistors configured such that a current through one transistor is mirrored in the collector of the other as a constant current. It's typically used in various bias circuits such as biasing the internal stages of an operation amplifier. (See https://en.wikipedia.org/wiki/Current_mirror for more info).