I'll take a shot at this, though it's a bit difficult to explain. OK.
Let's say you've got an array of pixels:
12345
67890
ABCDE
If you try to draw a single black pixel line at 45 degrees on
a white background it's going to hit parts of, say,
45
89
AB
But pixels are indivisable, so each of those pixels is either on
(white) or off (black). Anti-aliasing attempts to correct for this
by painting the various pixels touched by the line in various
shades of grey. When viewed from a distance, the greys blend
nicely and the line appears much closer to the desired result.
This approach minimizes the "jagged line" affect when lines or
edges are at some angle other than horizontal or vertical.
So..."aliasing" is just what happens if you don't have some sort
of "anti-aliasing" technology to solve the problem.
All in all, a relatively simple concept...but difficult to explain!
Dave