Most airlines overbook flights. Although tourists with heavily discounted tickets are pretty much tied to specific flights, full-fare business travelers are free to change their plans -- and they often do so.
Airlines are rather sophisticated at knowing which flights can be overbooked, and by how any seats. Usually, overbooking simply means that flights are full, even if some ticketed passengers didn't show up.
When more passengers show up at the gate than the capacity of the aircraft, the airline asks for volunteers. A typical offer would be a $300 travel voucher per passenger and a reserved seat of a later flight on the same airline or on a different airline. Usually, there are eager volunteers who are thrilled to accept the offer. Voluntary bumping hurts nobody. The airlines win because they can sell more high-fare seats. The volunteers win because they'll have free air travel on their next vacation.
There can also be cases of involuntary bumping. That's called denied boarding. It's quite rare. In the case of denied boarding, the unlucky passengers are entitled to real money, not just airline vouchers.
I wouldn't worry about denied boarding. It's never happened to me or to anyone I know.
On the other hand, delays and flight cancellations are much more likely to mess up air travel. These can be due to weather, mechanical problems, crew shortages, late aircraft arrival from another city, and air traffic control. Always allow a comfortable time cushion to allow for delays. For example, I would never book a flight to arrive just a few hours before a cruise or a wedding.
