While there are several different definitions of escrow, they all encompass 1) a contract between a client, trustee, or debtor and a broker, lawyer, or bank/creditor, and 2) that the client, trustee, or debtor pays the broker, lawyer, or creditor in order to have that money dispersed at a later date for a specific reason.
For the purpose of your question, the debtor that owns the mortgage basically has funds put aside by the bank for the purpose of paying the property taxes and insurance to the government. It is required from nearly 60% of all US homebuyers to have an escrow account due to existing federal regulations on homeownership.
There are pros and cons to having an escrow account.
An easy comparison to help you further understand escrow accounts is payroll tax withholding deductions from your place of employment. In this case, an employee earns an amount of money from working, and a portion of that money is deducted, in point of fact, held in escrow by the employer to later be distributed to the IRS and other state tax agencies. Just as in the case of (some) mortgages, escrow is optional, and employers may select to have no withholding and choose to pay in one lump sum at tax filing season.
The problem is, of course, that many people tend to live paycheck to paycheck and have poor spending habits. As a result, federal regulations make escrow accounts mandatory for all those who take out government-insured mortgages through offices like the Federal Housing Administration (FHA) or those who fail to make at least a 20% down payment on the price of the home.
While escrow does help most homeowners with budgeting taxes and insurance payments over the course of 12 months, it also provides a negative, a variable rate effect, even on fixed rate mortgages. So, whether you have an ARM or an FRM, an escrow could make your mortgage payment volatile due to variable future increases in both property taxes and homeowner's insurance, due to natural disasters ("Acts of God") affecting the area or the home, claims filed against the mortgage owner, tax increases, etc.
Once the mortgage is paid to 80% of its value, the homeowner has the option of closing the escrow account; however, once the mortgage is paid off in full, the contract between the bank and the debtor is fulfilled, and the escrow account is closed. Then, the homeowner is directly responsible to all state and federal agencies in regard to taxes and insurance payments which were held in escrow.
It is advisable once the escrow account is closed to open a bank account, or set aside the same amount of money as your old escrow payments each month so that you do not get hit with huge tax and insurance bills at the end of the year. I hope that I helped answer your question!