It became a catch phrase for Japanesepod101 for a while. I can't explain it very well, and it's explained very well in that lesson, so I'll just let you listen.
もういい = もう良い that's enough, enough already!
もうええ i haven't heard this, but in the kansai dialect いい (good) is ええ so might be the same thing as above.
萌え (もえ not もうええ) is the word in the maid cafe lessons.
it's often said stretching out the final vowel sound, so you might see some variations like 萌えぇ or 萌え~!