What does "pushback" refer to?

Pushback is the amount of time your cast time is "pushed back". This happens when you are attacked when casting any type of spell or skill, thus lengthening the time it takes to cast that spell. The reduced pushback means that the attacks will have less of an impact on your casting time.

The attacks also affects channeled spells/skills. It will cut out chunks of the channel.

In SWTOR, your character will have abilities in your advanced skill tree that will take time to take effect. For example, if you are a Sith Sorcerer and cast "Lightning Bolt", you will see a meter pop up on your screen with a bar sliding from left to right. When the bar reaches the right side, the lightning bolt will be thrown at the target.

"Pushback" happens when you are attacked BEFORE your meter has reached the right side. If you get struck, shot, etc. while waiting for your lightning bolt to be thrown, you will see the bar slide BACKWARDS a bit, that is "pushback".

Therefore, when some skills say they will reduce pushback, it means the bar gets moved backwards less, giving your ability a better chance to be completed and executed.