A cross-ship is a
method some companies will use when you want to return a
defective product and can't wait for a regular
exchange to process.
Lets say you order a
video card. It arrives, you pop it in your machine, and your speaker lets loose the dreaded one-long-two-short beep (assuming you're using an
Award Bios, anyway) of No Video Adapter.
Now, you'd rather not wait the two weeks or so it can take for an exchange to process. You want your video card, preferably
yesterday. So you call the company you ordered from, get an
RMA, and ask for a cross-ship. They charge you for an additional card and send it out to you right away. When they receive your return, they
credit you back. There are some companies who will do this without the additional
charge, but not terribly many.