Homing Weapons are ones that when fired in the proximity of an enemy, it will "search out" the opponent, as opposed to simply going in a straight to where you pointed with your target reticule. The "levels" of homing are different; some weapons home in on opponents faster or slower that others and they can turn and change direction faster or slower than others. However, most weapons home in and change direction at similar speeds, with the exception of the Bubble Blaster.
Homing bullets fly at slow speeds, allowing for skilled players to evade them with the use of agility. It was probably added to prevent overpowered these weapons; and so that it can quickly adapt to any new changes in the location of a player, rather than simply flying by it too fast to even start to home in.
However, homing weapons need a certain range to "sniff" out their prey, and if they can't find anything to home on, they will just arc downwards or "fizzle" out when they've flew to their range limits. It's a good idea to aim first, then let the weapon do the work once it is in range.