There is massive variation in what words people use and a lot also depends on the type of teaching and level at which she is riding, but there are also some which are pretty universal I think, I'll try and list a few and others can chime in if they understand them differently perhaps
Contact - is the connection from your hand to the horses mouth via the reins/bit
Leg on - application of pressure from the lower leg
Sit up! - they are looking for alignment of the head, shoulder, hip and heel vertically (not leaning forward/back)
Change the rein - is when you go across the school (often across the long diagonal) and go in the opposite direction
Change the diagonal - when doing a rising trot you have to 'rise and fall with the leg on the wall', its to help the horse balance, as the wall/outside side fore leg goes forwards you rise, as it comes back you sit
Serpentine - is a serpent shape you ride, it can be 3 or 4 loop (or more or less) and is like some S's joined together when viewed from above
Markers - are the letters around the edge of the school, they are in a set order so no matter where you go they are the same
Halt - is to stand still
Gait - is the way which a pony moves which is also related to their speed eg walk, trot and canter
I hope that's helpful