What is the meaning of legal term, "This contract becomes effective upon full execution"?

Certain equitable rights may be available to enforce the agreement.

"Full execution" usually means that all the parties to the contract have to sign it. There are some contracts, however, that need only be signed "by the party to be charged," meaning the party that has the obligation in some way to act.  Some contracts do not have to be in writing and if the elements of the contract are there - terms, consideration, etc. - then the courts can uphold the contract and force one of the parties to uphold the terms.  Some contracts have to be in writing or they violate what is known as the "statute of frauds."  An example here is a contract regarding real estate.

You should seek help from an attorney in your area, especially if money has exchanged hands and one of the parties has not executed the agreement.  The type of contract and its terms must be read in light of the actions of both parties.  Good luck.

"Full execution" would be signing by all the parties to the contract. Often contracts are enforceable as soon as one party signs; i.e. say I'm a freelancer and I send a contract to a business for my services--once they sign it, I can start working and hold them liable even before I countersign. However, if a contract very explicitly says that it's only enforceable upon "full execution," it would be very difficult, if not impossible, to enforce the contract until signed by both.

However again, if money has changed hands, then even if the contract is not enforceable per se, at the least, the party that gave the money should have a good case for either demanding the money back or getting an amount of performance/goods/services/etc. equal to what was paid. The mere fact that the contract was not mutually signed doesn't allow one party to simply pocket money of the other.