'At your pleasure' is a quite formal way to say 'to do something when you want to and in the way you want to'. So maybe you want someone to look at and correct something you have written but you don't want to seem pushy so you say 'please, read it at your pleasure.' You can also use 'at your leisure' which means when it is convenient for you/ in your own good time.

I never use this phrase.

It's better to use, "my pleasure" sounds more personal

hello, as in my language we say at your pleasure when somebody do a favor to others.