Having never played any game in the series before, I am intrigued by the name. Is it ever explained in the third game? If not, what's it meaning? (spolier-less as possible, if possible)
The "mass effect" is the (psuedo-)scientific principle behind most of the technologies in the series. For instance, the "mass relays" allow faster than light travel by exploiting the mass effect.
It's also the reason why weapons have unlimited ammunition (what you're actually doing is "venting a heat sink") and the way in which all of the biotic powers work.
It's explained in the introduction to the first game of the series:
Although it's a spoiler for the first game, by this time in the series we know that the technology was not invented by the Protheans (as was thought at the time of ME1) but is in fact far older. The galaxy's continual dependency on the mass effect is one advantage that the Reapers tend to exploit.
It's in your codex, under Technology. The Wiki also explains it and contains the codex except: