About 99% of barrels are made up of one a few different types of steel alloy -- of these, the choice is pretty much between Chrome-Moly steel and Stainless Steel.
Chrome-Moly - This name is used to describe a broad family of steels, the most common in use for the AR are 4140 and 4150... the 41xx indicates the AISI-SAE numbering for Chromium-Molybdenum alloy (ergo the name Chrome-Moly), these steels are alloyed with about 0.50% to 0.95% Chromium and 0.12% to 0.30% Molybdenum. The second part of the number indicates that percentage of Carbon (in tenths of a percent). Therefor 4140 is about 0.40% Carbon and 4150 about 0.50% -- the extra carbon in 4150 makes the steel a little tougher and it resists heat better... but it is harder to work and machine.
4150 is one of the "MilSpec" steels... another that is used in a lot of military barrels is CMV (Chrome-Moly-Vanadium) -- as the name implies, this is a chrome-moly steel (very close to 4150) with the addition of about 0.20% to 0.30% of Vanadium. CMV is reported to perform better under high heat.
Carbon steel barrels (chrome-moly) are the bread and butter of barrel materials for the AR, chrome-moly has made great barrels for many years and will continue to do so for many more. The only real downside to carbon steels is that they are prone to rust and corrosion problems.
Stainless Steels - We all know stainless steel, very high levels of chromium and nickel make these steels very resisitant to rust and corrosion, they are used in nearly every type of manufacturing around... the most common choices of stainless for a barrel are 410 and 416. There are a few "families" of stainless steel, but all of that is really academic to the discussion -- but 410 and 416 are Martensitic steels... simply they have lower percentages of chromium than other types of stainless steel.
The most common stainless in use for AR barrels is 416, this steel is plentiful, not expensive and machines nearly as well as the carbon steels -- 416 is rather strong, and has decent corrosion resistance; however, it is one of the least corrosion resistant of the stainless steels. Another choice barrel makers offer is 410, it is a little tougher and more corrosion resistant, but is harder to machine.
Grade 630 stainless, often called 17-4PH, is a great steel that offers excellent corrosion resistance and hardness. 630 is tough, but machinable, and tempers well. It is a precipitation hardened (PH) or age hardened steel and does not distort significantly during the hardening process; however, one consideration for the use of 630 is that the steel manufacturers do not recommend using it for applications that will expose it to cycling temperatures above 700 (f) -- In some cases this is not an issue, however in an AR that may see "heavy fire", 630 (17-4PH) is not a great choice.
So which is better, CM or SS? Again, this depends on what you want/need... a few things that seem to hold true about the two are that: CM barrels may take a little longer to break in and can be more prone to copper fouling; Due to the way the metal erodes in the throat area, the acuracy of CM barrels tends to degrade at a more steady rate, where SS tends to fall off quickly towards the end of its life; The throat area of CM barrels can work harden, this makes recutting the chamber and "bumping" the barrel back difficult -- but AR barrels can not be bumped back anyway (due to the gas port); SS barrels tend to be more prone to scratching but naturally is better at resisting corrosion (over an unplated CM bore); Many barrel manufacturers do not recommend using SS in sub-zero cold; Either SS or CM is capable of the same accuracy and will have about the same service life.