They will replace your broken PS3 with a fixed and refurbished unit (IE. a PS3 someone else sent in earlier) and mail it back to you. If they are good, they will let you keep your HDD (or transfer the data to the new one).
Most hardware repairs (that you send in) are dealt with this way. Essentially you don't get back the same PS3 that you sent in, but it should be an identical model or greater if they don't have yours available.