For analysing , whether a MOS is ON r OFF(sat r in active), v need a reference voltage , above which the condition changes... i.e) when Vgs<Vds (OFF) and vice versaa...
the Vt depends on fabrication , Ambient temp...
For more info refer Sedra...
Vt of a MOS determines how it behaves... it controls the current, when the MOS turns ON or OFF ..... it mainly determines when the MOS enters saturation or triode region or cutoff region and the biasing and other things can be calculated only if Vt is known......