Codeshare is a co-operative arrangement whereby airlines carry passengers whose tickets have been issued by another airline. The intent is to provide passengers with a wider choice of destinations than any individual airline might offer on its own.
When you book a codesharing flight, your ticket will bear the flight number of the airline through which you booked your travel, though some legs of your trip will be on flights operated by another airline and bearing a different flight number from the one printed on your ticket.