If you have a contract with someone, you expect them to fulfill it.
If they don't, you have several different options. You can choose to let the other party out of the contract, renegotiate for a new contract that you can both live with or demand a legal solution. One of those potential solutions is called specific performance -- and it's what you generally seek if you want the court to enforce the terms of the contract.
Of course, like most legal issues, it isn't quite that simple.
Specific performance is not usually a preferred remedy. It's generally less favored than paying money to compensate someone's losses for the broken contract. However, there are times when it's considered the only fair solution because money wouldn't serve to make the damaged party "whole" -- putting him or her back in the same basic position as before the contract was breached.
In real estate, for example, sellers sometimes try to back out of a deal. If they're lucky, the buyer may just accept any earnest money they put down back and repayment for any expenses they incurred -- like a home inspection. However, most buyers will want the house sale to go through and may demand that the court enforce the agreed-upon sale.
Any unique item could become the subject of a lawsuit demanding specific performance of a contract, not just houses. For example, imagine that you signed a contract to purchase an estate's collection of fine art. Then, one of the heirs decides that he or she doesn't want to part with some pieces. Because the pieces are unique, money can't adequately compensate you for the paintings that you were promised. You can ask the court to enforce the sale.
On the other hand, you generally can't force someone into specific performance in a service contract. That would brush up against the Constitutional amendment prohibiting involuntary servitude.
For example, imagine that you hire a cleaning company but the cleaner later balks at the task and refuses to do it. The court wouldn't enforce the contract. Instead, you would have to determine what financial loss you incurred because of the breach of contract -- such as the difference between what the breaching cleaner was supposed to charge and the cost you eventually had to pay -- and ask the court for that instead.
Source: FindLaw, "Breach of Contract and Lawsuits," accessed Feb. 16, 2018