What does "Aggro" mean?

Aggro as a term originated in MMO's, but its usage has spread considerably.

Originally it was coined to describe any creature who would attack you on sight. So an "aggro" mob was one who would attack without being provoked, as opposed to one who wouldn't attack unless you attacked it first. The related usages here are "aggro range" or "aggro radius" which is the distance at which the mob will attack, and "aggro chain" which is whether or not the mob will bring his friends along, even if they are outside of normal aggro range.

As the games evolved "aggro" became the state of being attacked. If you were being attacked, you "had aggro", and if you did too much damage to something and it started attacking you instead of someone else you "stole aggro". If you did something stupid you could have "too much aggro" which meant too many things were drawn to attack you.

In your example, he's saying that the unit AI can be exploited because they don't chain aggro, so you can move into their aggro range, and individually "pull" them from their groups and eliminate them one at a time.

It means that you move closer to enemy forces (may be slightly attack 'em) and move back.
If your opponent does not react properly then only couple of units will "aggro" and start moving to attack your units. So you can easily pick them alone.

i.e. as terran you can aggro enemy to go into range of your tanks

you can also check wiki. Starcraft's AI uses distance and type of unit to determine what to attack.

"Aggro" is a shorted form of aggravate, meaning to annoy someone or something so it will attack you.