Escrow is a third party that assists in the exchange of real property from one person to another.
When a buyer and seller agree on price and terms through a real estate contract escrow is then opened with instructions and a deposit from the buyer. An escrow officer will manage the transaction and remain an unbiased third party.
Some of their responsibilities include coordinating lender funds, distribution of funds, managing deposits, documents and recording ownership changes. Other common practices are that the buyer will order title insurance and the escrow officer will obtain a preliminary title report. The escrow officer will manage the contract's contingencies and coordinate for services that include: flood insurance, home insurance, inspections, financing and repairs.
It's helpful to have an experienced escrow officer managed so many of the complexities in a transaction and remain unbiased. The National Association of Realtors has a great article that elaborates on escrows.