In the windowing design method for FIR filters, the impulse response for the desired frequency response filter is selected with a window. Typically the desired frequency response is a rectangular function in frequency (a brickwall filter, pass a group of frequencies and block the rest), in which case the ideal impulse response is a Sinc function. In this case, the transition in the frequency response maps to a -6 dB cutoff after the windowing operation which will be half way between a passband edge frequency and stopband edge frequency.
The graphic below demonstrates this for a rectangular window. For other windows, the transition band will increase for a given number of taps, but the relationship between $f_c$ in the desired rectangular frequency response and $f_c$ that is midway in the transition band still applies.
For other design methods such as Parks-McClellan and Least Squares, the passband edge and stopband edge is provided to the design algorithm. The resulting 6 dB cutoff will similarly be half way between the passband edge and stopband edge. Generally it needs to be clarified as to what we mean by "cut-off" as this can refer to a -3 dB cutoff or -6 dB cutoff (or any dB cutoff).