A double spend is an occurrence when somebody tries to spend the same bitcoins more than once. Realistically they can only happen when someone accepts a transaction without waiting for at least one confirmation, or if an attacker controlled more than 50% of the network’s hashing power.
Most miners’ software will check for double spends before including a transaction in a block. However, they have no obligation to do so, and if a second transaction was published with higher fees attached, they may decide to include the second transaction instead, thus making the originally transaction the double spend, and therefore invalid.
Preventing the double spend is the specific problem solved by the blockchain allowing Bitcoin to work without a central authority. Each confirmation makes it exponentially more unlikely that the transaction will be double spent during a blockchain reorganisation.