Slow and fast filter
In the simplest terms, the slowness or fastness of a filter refers to its time domain characterization. Specifically a fast filter will have a short impulse response so that the output goes to steady state as quick as possible in time, whereas a slow filter will have a long impulse response, whose steady state output occurs after a longer delay, so that it will not be responsive to transient changes in the input.

Now according to the time-bandwidth product feature of LTI filters (which is based on a Fourier transform property) if a filter has wide frequency support, then its time support will be narrow, and vice versa. As a consequence, low cutoff frequency filters will have narrow frequency support and hence large time support. But a large time support is equivalent to long impulse response which is stated to be a slow filter as above. 

Therefore a low cutoff filter (a narrow frequency support) will be a slow responding one, whereas a larger cutoff filter will be fast responding one.