Logic level refers to the input and output voltage levels of digital logic, which is often 3.3 V or 5 V.
Logic level is relevant when driving MOSFETs directly from a digital output. Previously this was often 5 V, but today's logic ICs often operate at 3.3 V or lower. Power MOSFETs often need higher gate voltages to drive the rated current, and most manufacturers filled the gap by producing several logic level MOSFETs with a VGS(th) of 2 V or less, which can drive several amperes at 3.3 V.
Logic level is also important when connecting logic ICs operating at different supply voltages.