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Logic level refers to the 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, 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 $V_{GS(th)}$ of 2 V and less, and which can drive several amperes at 3.3 V.

Logic level is also important when connecting logic ICs operating at different supply voltages.

Further reading
Logic signal voltage levels information on All About Circuits