RAM stands for Random Access Memory (which differentiates from other types of computer memory which only allows you to see stored values in a particular order.)
It's pretty much the only computer memory you'll hear of these days. You use it to hold the programmes you are running, and to hold any data the programme needs. And these days, with things like mobiles not having a hard disk to store all your apps and suchlike, it is also used for that too. Your mobile will hold some RAM internally, and most mobiles now allow you to insert a memory card that holds more.