A collection of a million pixels or picture elements. These are the individual coloured dots which represent a digital image, the more of them you have contained within an image, the higher its potential resolution becomes.
Camera sensors with many megapixels are often able to capture more image detail than those with fewer. Be wary of assuming that more megapixels means better quality photos, though. Cramming more pixels onto the same-size sensor usually reduces quality and the lens also plays a big part in quality.