Well by definition: it is A trust account held in the borrower's name to pay obligations such as property taxes, home owners insurance premiums and flood insurance (if required).
Do lenders require it?
Many do yes and for good reason. If your home is destroyed by a fire, the lender will have lost his collateral.
If you do not pay your property taxes, the government can foreclose on your property in order to get the owed taxes and again your lender could lose the collateral. 
So obviously your lender wants to make sure your insurance premium and property taxes are always paid!
How does it work?
Your bank or mortgage company (or company they have that does the 'serving'), collects your property taxes and your insurance premium in a special account. This money is then used to pay your taxes and insurance premiums when the as they become due. The lender estimates the balance needed to be kept in this account based on the estimated amount necessary to pay the taxes and insurance throughout the year.
This amount is then added to your monthly mortgage payment. At closing the buyer pays "Pre-paids" which are used to start up this account.
Can the Lender ask for more money in the Escrow Account than needed?
A little. RESPA (The Real Estate Settlement Procedures Act) sets a limit on the amount that a lender can require a buyer to put into an escrow account to pay taxes and insurance. The lender or servicer will review the amount in the escrow account annually and if there is an excess of $50 or more must be refunded. If there is not enough - the lender will ask for more money to be placed into the escrow account.
RESPA doesn't require lenders to set up escrow accounts but, some government loans (FHA and VA loans) may require escrow accounts as a condition of the loan.
Escrow accounts usually will include a "cushion" or extra amount which helps ensure that the lender will have adequte funds to pay the taxes and insurances. There is no cushion required by RESPA, however it limits the amount of the cushion to 1/6th of the total amount of items paid out of the account, or 2 months of escrow payments.

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Good post. Many buyers do not understand the concept of an escrow account. I think you should post this on localism as well.