Antialiasing/AA is an image processing technique which helps remove the harsh edges produced by non-horizontal or non-vertical lines displayed on 2D monitors. Due to the technology of our monitors (i.e. the fact that we use block sized pixels), the smallest sized piece of information that can be displayed is actually a block in shape. Due to this when a curved edge is shown, there will be a jaggedness to the rounded features, as well as when a line is not in the perfect horizontal or vertical position, a jagged change will occur because there is a fixed finite number of positions that image information can be produced on the display device.
For example, to draw a slightly angled line on a screen you will get something like this:
_________---------------
Where there is a clear jump in the height of the line.
Antialiasing scans for those harsh jumps, and then changes the pixels leading up to the jump and the ones after the jump to lessen the harshness by changing the color of the pixels around the jump into the weighted color interpolation between the two pixels (in other words, if 10% of the line would really be in the pixel, but the other 90% of the pixel is suppose to be the background color, then the pixel will have its color adjusted 10% closer to the color of the line, but still be 90% like the color of the background).