Some of the benefits are just wanting to know what the 1st, 2nd and 3rd largest values in a data set are. It can also be nice for conditional formatting before they had the feature of Top N or Bottom N because you could use conditional formatting to color any number >= say the top 3 by using the large function. It can also be really useful in summing the top N records or bottom N records like so:
Entered as an array formula with control+shift+enter, this will sum the top 3 values and the bottom 3 values. You can also make it a little more dynamic by using rows function:
Hope that gives a little more insight into what they are used for.