Absorb is the ability of non-fragile defenders to take damage and then survive unscathed, thus able to take the same damage again next turn and survive again. Absorb is extremely powerful, as 307th excellently explains in his guide "The Standard Style".
Soak is defense that is bought simply to die and not to absorb.
Threat means damage or chill that your opponent doesn't necessarily want to actually deal. For example, a Drake provides 2 real damage and 2 threat.
Vigilant units are ones that can block while performing some other useful function, such as Xeno Guardian which can block while attacking (note that Steelsplitter cannot).
Resource abbreviations: E means energy, G green, B blue, R red, and X means attack. Gold is denoted just by a number. So for example, we would say that Centurion costs 18GGBBR.
HP means health, but you knew that unless you've literally never played a video game before :P
Overdefending means buying more defense than you need, not anything you do during the actual defense phase.
p1 and p2 refer to the players who go first and second.
BSO = Base set only.
Base + x means the set of units including the base set and the listed units (or the listed number of random units), eg. Base + Borehole Patroller, Base + 5.
The base set units are commonly referred to by the first letter of their name. Eg. T is more efficient than S. Note that some of these conflict with the resource abbreviations.
To refer to turn numbers, we often say things like t4, etc.
Line notation: Although many openings have names (see my opening list), people often still refer to them by specifying every move. So for example, to open DD/DA as player 2 is to buy 2xDrone, then Drone+Animus (this is the common opening 'Fastimus'). We can also use turn numbers to jump into the middle of a game, like: p1 should play 6: WEB there.
an autowin is a set where one player (p1 or p2) has an unbeatable line. Technically every set is an autowin by this definition, so we usually only use it to refer to sets where the line seems obvious to the point where the other player simply has no chance of winning if the opponent plays half-decently.
A legendary unit is a unit that has only 1 supply.