An accelerometer is an electrical device that measures acceleration. Acceleration is the rate at which velocity changes over time and is measured in units of length (L) per unit time (T) squared: L^[1]*T^[-2]. Typical accelerometers measure acceleration along 1, 2 or 3 axes. An unconstrained rigid body has 6 ways it can move (degrees of freedom) and accelerometers are normally used to measure 3 of these: translations along each of 3 axes. The other degrees of freedom (rotation about 3 mutually perpendicular axes) are usually measured with gyroscopes.

An accelerometer sitting on a table with its axis of measurement pointing straight up and down will record ±1, meaning that the acceleration of gravity (1g) is detected as straight down (unless you are holding it upside down). An accelerometer in free fall with record 0 in every direction.

You can get a wide variety of accelerometers at Sparkfun: http://www.sparkfun.com/commerce/advanced_search_result.php?keywords=accelerometer&x=0&y=0&search_section=products

Another choice is the Wii Nunchuck (A cheap Accelerometer (16$) with I²C interface, 2 Buttons and an Analog-Stick)