In more detail
In a home purchase, escrow holds the buyer's deposit and the paperwork until closing, when the funds and the title change hands together. After closing, many lenders also keep an escrow account: part of each mortgage payment goes into it, and the lender pays the property tax and insurance bills when they fall due. Once a year the lender reviews the account against the expected bills; in the US, federal rules let it hold a cushion of up to one-sixth of the year's payments (two months).
Why it matters
This is why the monthly payment can change even on a fixed-rate loan: if taxes or insurance go up, the escrow part rises, and any shortfall from the past year is usually spread over the next twelve payments.
Example
Property tax of $4,800 a year and insurance of $1,800 a year add (4,800 + 1,800) / 12 = $550 a month to the mortgage payment. If the tax bill rises to $5,400, the escrow part becomes $600. If last year's account ended $600 short, the lender adds $50 a month for a year, so the escrow part is $650 until the shortage is repaid.