Define high current amp?

This may be a very rudimentary question, I'm just trying to learn:

I've fallen in love with electrostats, and am contemplating Magnepans or Soundlabs. The Martin Logan's I've heard are dark and ill defined to me (just my ears' opinion).

In selecting upstream equipment, I keep reading on these forums about planars requiring an amp with high current output to do their best.

In what specification for an amp would I be looking to select a high current amp? Is there a particular threshold of this spec which defines high current vs. low? I'm a little confused, as I have an old Yamaha integrated, and have been told a couple of times it puts out high current, but would like to know how to definitively compare this characteristic of different amplifiers.

Thanks in advance.