Why On the resistance range a multimeter supplies its own small test current from an internal battery and expects the circuit to be unpowered, so its input is a low-impedance path rather than the high-impedance input used for volts. Connecting that low-impedance ohms input across a live voltage source pushes far more current through the meter than the ohms circuit was designed for, which can burn the input, the range resistors, or the fuse. Always de-energize the circuit and switch the meter to a voltage range before touching live terminals.
Watch out Measuring resistance while set to volts simply gives a meaningless or zero reading; nothing is harmed because the voltage input is high impedance and passive.
Ohms mode is for dead circuits only: ohms plus live volts equals smoke.