This term refers to the size of an image, usually in reference to a photo from a digital camera or camera phone.
Megapixel means one million pixels. The resolution of digital cameras and camera phones is often measured in megapixels. For example, a 5-megapixel camera can produce images with five million total pixels.
Since pixels are usually square and form a grid, a 1-megapixel camera will produce an image roughly 1200 pixels wide by 900 pixels high.
Multi-megapixel images (2 megapixel or greater) are often larger than the resolution of a phone display, so a 5-megapixel camera will not make much difference compared to a 3-megapixel camera if the photo is only viewed at full size on a phone.
Rather, high-megapixel cameras are most useful for taking photos suitable for viewing on a PC and/or printing.
However, more megapixels do matter when viewed on a phone, when zooming in or cropping a photo. For example, some phones with 20 or more megapixels let users "zoom in" without losing quality, without an optical zoom lens. They do this by simply cropping a high-quality 8-megapixel photo from the center of the 41-megapixel image captured by the camera (for example.)
Photos with more megapixels are larger in file size, and therefore can take longer - and cost more - to send over the network at full size.
Most cameras and camera phones have an option to take photos at lower resolution (smaller), if desired. This is useful for taking photos that will only be sent via MMS and not transferred to a PC or printed.