I know that when I kill various enemies, I get experience points that help me level my characters. However, sometimes I see "Tech 1pt" or "Tech 2pt" after hitting (not necessarily killing) an enemy. What does that mean? What does "Tech" do?
"Tech" is bonus XP earned during a fight. It's generally awarded for succeeding in... Unecessary areas, to put it bluntly.
An example would be Wakka in the beginning. When he yells, "Take this!" and throws his blitz ball at you, you can hit it back to him for bonus XP in the form of Tech points.
There are several other ways to earn tech points (parrying an attack, exploiting an enemies weakness, etc.).
The Wikia gives a few more (better) examples than mine, though.