I've heard people in casts say "A-Move."
What does it mean?
I think it refers to "Attack Move"
When you click (or press keyboard key "A") attack, then click somewhere on the map, your units will move there and engage anything they find along in the way.
This is (in most of the cases) better than simply moving, since your units will retaliate to enemies instead of just walking into their fire.
BTW this strategy is a keypoint is the vast majority of RTS games ever created
"A-Move" is just short for "Attack Move". There are several ways to accomplish this in Starcraft 2, including literally hitting the "A" key and then left clicking (where the term was coined from), or by clicking the "Attack" icon inside a units command grid, and then clicking. In addition, according to the Starcraft wikia site, in SC2 you can hold control and right click on the ground to attack move as well.
If any enemies are encountered along the way, the group will attack that enemy until it is killed. They will repeat this until all encountered enemies are dead, then resume moving to their original destination.
Most times it is optimal to "A-move" your units, so in the event they encounter enemy troops while you are waiting for them to arrive, they don't just sit there, but instead retaliate. However, there are instances where it would be better to just move, rather than attack move, if you don't want your units to stop to fire (say running past a spine crawler at the choke of a base).
Other answers cover the literal facts of A-moving, there is also the implied connotation.
In addition to A-move meaning "attack move," it also refers to a style of unit control that's best described as fire and forget. If you attack-move your units into an opponent's base or army, you are simply telling your guys "Go over there and attack stuff." You are giving them better orders than just "move here," but you're not necessarily specifying focus targets or using special abilities.
This can be used in a positive manner, such as, "You're better off building your economy and just a-moving your army than you are babysitting your troops but neglecting your expansions." It can also be used in a negative manner, such as in @Ant's answer, "Instead of just a-moving your troops, you should micromanage them so they are more effective."
Hopefully this helps explain both the literal and implied uses of the term.
Also, a-move is used as an insult. Sometimes, when a zerg (z) player gets beat, even though he/she outplayed the opposing protoss (p)/terran (t), they will reply "a-move" or "1a-move."
They are trying to make the point that t and p require almost zero micro to beat a z, where as z requires heavy micro. This is one of the major reasons z say their race is the hardest to play. Of course, there are other reasons which is a whole other topic of conversation.
Btw, I am a z player myself and have insulted people this way. ;)
A-move means attack move.
When a caster says something like "MKP can A-move and still win the game" he refers to a huge advantage the other player cannot possibly compensate.
While every player attack moves into the other army, the term A-move usually means that there will not be any further micro during the battle. You can either watch the armies clash or go back to your base and Macro.
Sometimes the term A-move is used to refer to an army in the sense of: "He has an A-move army". This is equivalent to a "Ball", like the "Terran Ball" or the "Protoss Ball". This means the army has reached a good unit composition with a critical mass and it will crush almost anything the opponent can throw at him. An A-move army cannot consist of caster units, as these require further micro. A good example for an A-move army is Marine Marauder Medivac, you Stim and A-move and that is it.