An airline may refuse to allow you to board for various reasons. One of the major reasons is that they have overbooked your flight. Overbooking is a common industry practice and airlines do this as they rely on some passengers not showing up. When an airline overbooks, they initially ask for volunteers to not fly but will sometimes 'bump' people off a flight. If you are 'bumped' off a flight, you will be entitled to compensation and refund of the flight ticket/re-routing to your destination and assistance.
To be entitled to compensation three conditions need to be satisfied: