A term in contract law, it means more or less exactly what you'd think it means: it means that the terms of a contract will only come into effect if a certain condition does (or does not) come to pass.
A simple example then. I sign a contract with my friend that if either of us wins the lottery, we'll split the winnings with the other 70/30. The condition precedent is winning the lottery. Otherwise, this contract just sits in a desk drawer, worthless.
The more common example of this is that one party of the contract must fulfill their obligations before the other party is obligated to fulfill their own. For example, if you hire someone to paint your house, you may choose not to pay the painter until the job is done. Thus, the painting of the house becomes a condition precedent to the painter getting paid. However, in cases where the condition precedents are clearly defined within the contract itself, they are usually referred to as contingencies instead (and thus are less ambiguous and less subject to breach.)
Contrast with a condition subsequent.