What is the difference between a nonretriggerable and retriggerable One Shot?

In a retriggerable MMV a new trigger during a pulse will restart the pulse time, and thus extend the current pulse.
If the pulse time is 10 s and you would retrigger 6 s after the first trigger you would get a 16 s pulse.

In a non-retriggerable MMV the second trigger will be ignored and you'll get a 10 s pulse:

This concerns the circuit's response to additional trigger pulses while it's in a triggered state (is outputting a pulse). In a retriggerable monostable, additional input pulses will extend the output pulse by keeping the circuit in the unstable state, while in a non-retriggerable one they will have no effect. See wikipedia.