A technique used on a grey-scale or colour bitmap display to make diagonal edges appear smoother by setting pixels near the edge to intermediate colours according to where the edge crosses them.
The most common example is black characters on a white background. Without anti-aliasing, diagonal edges appear jagged, like staircases, which may be noticeable on a low resolution display. If the display can show intermediate greys then anti-aliasing can be applied. A pixel will be black if it is completely within the black area, or white if it is completely outside the black area, or an intermediate shade of grey according to the proportions of it which overlap the black and white areas. The technique works similarly with other foreground and background colours.
"Aliasing" refers to the fact that many points (which would differ in the real image) are mapped or "aliased" to the same pixel (with a single value) in the digital representation.