I hope this comes out as understandable...

We use some of the light from the telescope and direct it to sensors that measure the wavefront distortion.

Traditionally, Adaptive optics without a laser required that a star brighter than 13-14th magnitude be within 30 arcseconds (1 arcsecond is 1/3600th of a degree) of the target you are wanting to observe. This requirement is only met by ~1% of the sky.

When starlight hits the atmosphere its flat wavefront is deformed and so it cannot be well focussed unles you deform it back to flat again... the angle at which it seems to come from also is distorted by air turbulence- hence the 'twinkling of a star'. To measure and fix the apparent 'movement' of the image does not take many photons, but to flatten the wavefront takes a fairly bright 'star'. The laser cannot be used to correct for the aparent rapid jitter in the position of the star (this is called 'tip-tilt' correction), but it does alllow you to correct the wavefront distortions. since the magnitude of the laser guide star is ~9-10.5 it allows you to position a bright wavefront reference star anywhere in the sky.

You still need a 'tip-tilt' reference star somewhere near your target- but as I said above, this star can be much dimmer- we have used 19th magnitude, so now we only need a 19th magnitude star near the target- this criterion is met by ~80% of the sky...

There is a lot more to it than that, but thats the quick version...