A fast recovery diode works the same way a normal diode does: i.e. forward voltage drop is 0.7 volts.
The difference is in the speed it ‘recovers’ when it goes from the forward to the reverse direction (i.e. from conducting to non-conducting).
In other words: in non-fast recovery diodes, the path between the anode and cathode is still somewhat conductive after the current that placed them in that state is gone.
A fast recovery diode is usually used in high frequency or fast switching (MOSFET) applications.
e.g. fly back diodes are often fast recovery types.