A 50 ohm terminator is just a little bnc cap that has a resistor (you guessed it, 50 ohms) between the signal and the shield / ground.
Basically, you need the terminating resistor whenever your cable is a 'transmission line' -- that is, the propagation time of your signal cannot be considered instantaneous. 1 meter of coax has a propagation delay of 5 nanoseconds and a round-trip time of 10 nanoseconds. If your signal changes fast enough that you cannot always consider the input and output to be at the same voltage you will have a problem due to signal reflections. The exact cutoff where you need proper termination depends a bit on your application, the driving circuit, and whether there are any intermediate 'taps', but basically even a relatively small fraction of a wavelength can cause problems.