In a nutshell here are some very basic definitions for anti-aliasing (AA) and anisotropic.
AA refers to jaggies. Lines that are not made exactly horizontal or vertical are actually made by small tiny squares. AA takes the “hardness†of the squares and adds shading to the valleys between the sharp points to make the line “appear†smooth. There are different rates on most of today's video cards that include 2X, 4X, and 6X. For each level of improvement it requires exponential calculations, which equals more demand on your hardware.
A note for gamers…AA slows down your computer. Turn it down or off for optimal performance. Also a good trick is to turn OFF AA and turn up the resolution. The higher the resolution the smaller the squares become and smaller the squares become the jaggies become smaller as well.
For more information on AA, here is a very good link with examples.
http://www.computerworld.com/softwaretopics/software/story/0,10801,71480,00.html
Anisotropic refers to the way that texture is presented to the user. Anisotropic comes in a few different rates on most of today's video cards including 2X, 4X, 8X, and some have 16X. Just like AA, higher the rate an exponential higher calucation is required to present the information of the texture to the user.
The best engine on the market for demonstrating this technology is the CRYEngine that is used in FarCry. The amount of detail within the texture is mind blowing. However, even with today's fast machines 3.0GHz, ATI's 9800 Pro and 512 MB RAM this is tough to use to the fullest. But if you want, crank up the anisotropic and run FarCry (don't play it because the beauty and the filtering will cause your machine to come to a very quick halt). But look around at the texture in the water, on the mountains, and even in the clouds. It is really beautiful.
A note gamers… Anisotropic slows down your computer and with fast moving games its really hard to focus on the detail. I like to use 2X to 4X anisotropic, turn off AA and turn up the resolution. This works very well on good resolution games that use textures, i.e. FarCry, Unreal Tourament 2004 (and 2003) and Generals. Generals is very texture intense so I lower it down to 2X or sometimes it off depending on how much is going on the screen at one time. Here is another tid bit of information. When playing Counter Strike turn off anisotropic and enter the DUST2 map. Look at the dust trail ahead of you where you can see a long way, notice where the texture of the dust becomes a blur in a circular pattern ahead of you. Now exit the program reset the anisotropic to the highest it can go (8X or 16X works best). Go back to the DUST2 map and take a look now. You should be able to notice that the dust texture is all around you now. The place where it went from texture to blur should've increased or disappeared altogether.
For more information on anisotropic, here is a very good link with very good examples.
http://www.extremetech.com/article2/0,1558,1152380,00.asp
Hope this explains why you had to turn down or even turn off AA and Anisotropic to play FarCry. And Half-Life 2 and Doom III is suppose to focus more on details. For a very funny article read this one on rusticles...
http://archive.gamespy.com/grudge/2004.04/2004.04.19_vote.shtml