Fred42Vid's answer is good (though the 1/4" jack is probably a balanced TRS). I wanted to add something, though; on a mixer, when you have both a TRS and an XLR, they sometimes have subtly different signal paths. Specifically, the microphone input is often run through a second op-amp to boost its signal by about 20dBu before the main gain stage (controllable with the gain knob). This is because XLR typically carries relatively weak "mic-level" signals, while TS/TRS typically carries higher-strength "line-level" signal.
Now, this line between "mic-level" and "line-level" is very blurry, and you may find yourself boosting a weak TRS input with the gain knob, while at the same time padding or turning down a hot condenser mic. I'm just saying that very often, mixer XLR inputs get their own preamp designed specifically to boost microphone signal to working line levels, while a TRS is assumed to already be at that level.
Apart from that, the main advantage to XLR over TRS, all other things being equal, is phantom power; it is typically sent from pins 2 and 3 of the XLR input, and not from the TRS (the design of a 1/4" plug generally makes sending power along it risky; there's no positive latching mechanism, and contacts for various elements of the connector can contact other portions of the plug causing shorts and other damage). Both of these jacks are used for balanced, low-impedance connections; you don't usually plug an unbalanced, high-impedance 1/4" TS plug into a mixer (though some mixers, especially for home studios, can even deal with that).