An astable is not 'stable' in either the low or high state - thus it is constantly changing from one to the other - low/high/low/high/low....
A monostable is only 'stable' in one state (say, for example, in the low state), so it starts off low, goes high once, and returns to low (and stays there) until triggered again.
A bistable is 'stable' in both low and high states, so when triggered, it goes from low to high, or high to low.