A pre-determined or pre-estimated sum included in a contract to set the amount of compensatory payment (damages) to be paid to the non-breaching party by whichever party to the contract breached his/her obligation(s).
When a person does not or cannot perform the obligations agreed to in a contract to which they are privy (i.e. breaches a contract), they are exposed to liability in the form of a specific performance order against them or, much more likely, an order for damages; so that the other party to the contract can be compensated for the breach of contract. A court is always in a difficult position when called upon to determine what the amount of those damages ought to be; the plaintiff asking for too much and the defendant too little.
A liquidated damages clause pre-determines the amount so avoids the necessity of leaving this to the discretion and judgment of a Court and also allows the party contemplating breach to properly make a cost-benefit analysis of the cost of that breach.