plain top is generally solid colors, quilt top is quilted maple guitar top which is usually transparent finish so that you can see the quilt top, Flame top is Flame maple which is the same thing as quilted maple but there is a diffrent look to the flame than quilt.
Ive had loads of guitars and Ive usually found that the plainer the wood (No flame or quilt) the better the guitar sounds. IMO its to do with the vibration passing through the wood and a plainer to vibrates and resonates more freely than flame or quilt. Some do look stunning though
I think plain top means the grain of the timber is reasonably 'plain' still a transperant finish though. I know this is the case with the Les Pauls anyway, the plain tops are bursts, the quilt tops are the same but a more detailed grain.
Usually it's maple top, along with basswood or maho body. This is to add some high end to the tone.

other than that, flamed maple are purely for aesthetics, and they look amazing.