Overbooking flights is a common practice by airlines, so if everyone who booked a seat turns up, there's a problem.
Here's the lowdown on your options...
Your rights if your flight is overbooked
If your flight is overbooked, the Denied Boarding Regulation says the airline must ask for people to volunteer not to fly 'in exchange for benefits'. If there are not enough volunteers, the airline can free up seats by denying passengers the right to board the plane.
If you volunteer to give up your seat, you're entitled to a refund or re-routing and also 'benefits' - which you have to negotiate with the airline. Note that there are no parameters as to what benefits the airline should offer.
If you don't volunteer, or can't agree 'benefits' with the airline, and you are denied boarding, you have the same entitlement to assistance and compensation as you'd have if your flight was cancelled. The only difference is that you are entitled to the compensation straight away.