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.
In the year 2148, explorers on Mars discovered the remains of an ancient spacefaring civilization. In the decades that followed, these mysterious artifacts revealed startling new technologies, enabling travel to the furthest stars. The basis for this incredible technology was a force that controlled the very fabric of space and time.
They called it the greatest discovery in human history.
The civilizations of the galaxy call it...
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:
Mass effect fields are created through the use of element zero. Element zero can increase or decrease the mass content of space-time when subjected to an electrical current via dark energy. With a positive current, mass is increased. With a negative current, mass is decreased. The stronger the current, the greater the magnitude of the dark energy mass effect.