Focus is the concentration a hunter's pet must expend to use its abilities such as Growl. From a player's perspective it is almost identical to the rogue's energy. By default the focus bar is full, with 100 points. When used, it regenerates fairly slowly (5 focus every second). The regeneration rate is not affected by being in combat.
The size of the focus pool and the regeneration rate are both constant - they do not increase with levels, and are not related to any statistics. As of patch 2.0, the 2 point Bestial Discipline talent will increase the focus regeneration rate by 50/100%.
During early stages of World of Warcraft development, hunters themselves used Focus as well. Back then, Focus only regenerated when standing still. However, this distinguishing feature was dropped before launch.