No mention of Anti Aliasing but I think most know that it gets rid of the jaggie edges. The higher level of AA you choose the smoother the lines. AA generally does work a graphics card quite hard.
Anti-aliasing works by darkening the edges of models so that jaggies are less apparent or gone. It shades the edges.
Computers display everything in pixels which are squares. Now, try drawing a diagonal line with squares. You can't. You can create a step-like "line" through the pixels, but that will look very jagged (hence the name jaggies)

A diagonal line is impossbile as it only uses parts of pixels (which do not worked that way, think of it as a lightbulb, you can't have one side lit and one side dark).

A line can be simulated by creating step like jaggiess. You get the illusion of an line, but it is ugly. Anti-aliasing solves this problem by shading the sides as seen below.

Of course, this is all done mathmatically with different colors (not just black and white) and puts immense pressure on the gfx card and/or the CPU (anti-aliasing use to be done on the CPU, but with the complexities of gfx, modern gfx cards built AA (Anti-aliasing) processing into the GPU.
The differences between AA off and AA on can be huge, though it does depend on other factors.
Without AA

With 4xAA

Of course, the amount of AA you use depends on the abilty of your gfx as it can be a huge performence heat.
AA levels range from none to 8x. Generally 4x is perfect.
Newer games like Half Life 2 have support for up to 8x AA