Basically means a new customer and not have had a trial or account with them before
Oh and according to the details on TCB you need to do the following
"To receive your cashback you must sign up for your first no-obligation free trial. In order to qualify for your cashback, you must add at least ten discs in your rental list and receive at least 1 DVD rental by post."
i took this offer thru topcashback it was ok till the time to cancel what a nightmare asian call centre kept me on hold would not listen to what i wanted in the end i had to call credit card cnmpany to block them.