How much water is too much water underneath the basement concrete?
To answer "how much is too much," if it's causing dampness in the basement, wet concrete, efflorescence, etc. then it's too much. If the only reason you know about it is because of the new hole, then I would monitor it over a few months.  It should eventually dry out.  If it doesn't then you might look at a sump pump.

As to what to fill hole with, fill it with gravel to about 4-6" below the floor surface, then finish with concrete to match the surrounding area.

It's also worth taking a look at the grading outside your house, water show flow away from your foundation.  Also make sure eaves are draining far enough away from your house.