current sourcing, current sinking
short version: current sources connect things to Vcc, current sinks connect them to ground.

longer version:
The following is a practical explanation of current-sources/sinks as used in microcontrollers &amp; TTL logic. For a more theoretical description, see the Wikipedia page on current source.

Some devices are very good at creating a connection to ground. (or whatever the lowest voltage is in the system, e.g. 0V)  Other devices are very good at creating a connection to Vcc. (or whatever is the highest voltage in the system, e.g. +5V)

Those devices that are good connecting to ground are called current sinks; those good at connecting to Vcc are called current sources.  Until recently (the last decade or so), it was unusual for integrated circuits to be good at being both.  Most were good at being current sinks but were terrible at being current sources.  So at lot of circuits were designed so all the chip had to do was connect to ground to make the circuit do its thing.  Many chips still have an asymmetric current drive ability and function better switching to ground than switching to Vcc.

To me a good example of current source and current since are the standard "switch" configuration of a PNP and NPN transistor.  A PNP is a good current source: you almost always connect its emitter to Vcc, and it switches it on/off.  A NPN is a good current sink: its emitter is almost always connected to ground and it switches the ground connection on/off.

Why you choose one over the other often depends on the capabilities of the parts available to you.  For instance, an RGB LED is often a "common-anode" type where the anode (positive lead) is connected on all three LED elements, so to turn on an element you need to connect its lead to ground.  You can use three pins on a microcontroller to do this (or three NPN transistors) and they would be acting as current sinks.