Contrary to popular belief, monetary damages are not the only form of relief when the other side to an agreement breaches your contract; there are circumstances where New York's courts will compel the other side to abide by its end of the deal.
This type of relief is referred to in legalese as "specific performance."
Specific performance generally is not an appropriate remedy when money damages are sufficient to protect the interests of the injured party, JMG Custom Homes, Inc. v Ryan, 45 AD3d 1278, 844 NYS2d 817. However, specific performance is appropriate where the amount of damages is difficult to ascertain, based upon the unique subject matter of the contract or the lack of an established market value, Van Wagner Advertising Corp. v S & M Enterprises, 67 NY2d 186, 501 NYS2d 628, 492 NE2d 756; JMG Custom Homes, Inc. v Ryan, supra.
One of the more common areas of law in which this relief is sought is with respect to the purchase of property, particularly where one of the sides to the deal wants the sale to go through - and the other (the defendant) wants to back out of the deal. As I'm sure you can imagine, there are any number of reasons that either the buyer or the seller of property would want to back out of the deal, such as a sudden uptick (or downward tick) in the property's value.
To that end, in the real estate context, in order to avail himself of specific performance, the buyer must demonstrate that he has substantially performed his contractual obligations and is ready, willing, and able to fulfill his remaining obligations, that the defendant was able but unwilling to convey the property, and that there is no adequate remedy available at law (i.e., monetary damages will not make him whole). ADC Orange, Inc. v Coyote Acres, Inc., 7 NY3d 484, 824 NYS2d 192, 857 NE2d 513; Huntington Min. Holdings, Inc. v Cottontail Plaza, Inc., 60 NY2d 997, 471 NYS2d 267, 459 NE2d 492; Yitzhaki v Sztaberek, 38 AD3d 535, 831 NYS2d 267; Fallati v Mackey, 31 AD3d 879, 818 NYS2d 341; see Lot 57 Acquisition Corp. v Yat Yar Equities Corp., 63 AD3d 1109, 882 NYS2d 454; Flowers v 73rd Townhouse, LLC, 52 AD3d 104, 857 NYS2d 146; Garnot v LaDue, 45 AD3d 1080, 845 NYS2d 555