If a plaintiff sues and ask for specific performance, what does it mean?

The normal remedy for breach of contract is an award of damages, that is the court will require the breaching party to pay money to the non-breaching party to put it (the non-breaching party) in the position it would have been had the contract been fulfilled.  For example, if you breach a contract to sell me a lawnmower for $300, and I have to spend $400 to buy a comparable mower from a store, the Court would award me $100 damages.  In some cases, however, where the performance the breaching party owes is something unique (like to convey a certain parcel of real property) the non-breaching party may seek the remedy of specific performance, which means that they ask the court to compel the breaching party to perform the contract.  So if you breach a contract to sell real estate to me, instead of seeking damages for that breach, I would ask the Court to compel you to honor our contract, i.e. sell the property to me on the terms provided for in our contract.