All it does on my multimeter is freeze whatever value it was reading at the time. When would I need to use this?
I rarely use the feature but for more precise measurements it can be useful. For example if measuring a sensor I might want to make a note that the meter reads 2.984 V and it's more convenient than trying to remember the value while I write it down on a piece of paper or enter the value into a spreadsheet etc.
Sometimes too I might be in a position where it's hard to read the meter output at the same time and I can rest my little finger on the hold while positioning the probes.
Some higher end meters also have an auto-hold type feature where once the reading becomes stable they will take the measurement and hold the display. That's a feature that I find much more useful because you don't have to keep your eye on the meter at all and they will beep when the measurement is done.
Some hold buttons don't do the hold until the meter sees a signal. So you press hold, turn to your circuit, and put the probes on whatever you want to look at; the meter triggers the hold, and you get the reading without having to look at the meter or have a third hand to press the hold button while you're holding the probes.