Escrows provide both buyer and seller with a 3rd party "stakeholder," and that stakeholder is licensed (in California) by the California Department of Insurance.
It's their responsibility to receive and disburse monies, record documents (done normally through the Title Company that you're using), provide each side with an accounting, and generally be "the neutral third party" in any real estate transaction.
While an escrow company cannot advise you of a particular course of action to take, an escrow normally can direct you to the proper professional to help you.
An escrow is especially important if you are a "for sale by owner," because an escrow company is the repository for loan and transfer of title documents that need to be held by a third party.
Escrows also work with title companies and lenders to verify ownership, notarize documents, and hold and verify down payments and initial deposits.
In the case of a property sold by real estate professionals, they will rarely allow a transaction without an escrow involved, since the escrow protects all parties to the transaction.
If you are selling or buying a property, the escrow will hold the deed(s) until such time as the monies are delivered to escrow, and then the escrow sends the documents to the title company for recordation. The escrow then disburses the monies once the deed is recorded, and the escrow is closed.
The reason this is so important should be obvious. Nobody gets the house until the money is delivered to the escrow, and the money is not handed over to the seller until the deeds are recorded. That way, everyone gets what he is supposed to, and nobody gets an unfair advantage.