Abbreviation for "adjustable rate mortgage". As opposed to a fixed rate mortgage, an ARM is generally offered at a low fixed initial rate which is adjusted relative to the prime rate or some other index every year or three or five. Good for the buyer if interest rates stay put or drop; bad if they go up.
They're popular because the initial rate is lower, allowing for a higher loan amount. This is expecially advantageous if you don't plan to live in your home for the entire length of the mortgage. They often allow you to refinance to a fixed rate mortgage after a certain amount of time (for a fee, of course) in case the adjustments aren't working to your advantage.