With the possibility of logging everything that goes on at the tables in online poker, there is of course also the possibility to input those logs into programs that calculate various things and can present statistics about your game, and tools to calculate odds, etc. This page lists some of the most common ones. None of the tools listed are by illegal to use or constitute "cheating" in any way, and most of the major sites have no issues with these programs. If you play on one of the smaller sites, however, you may want to check what's allowed and not allowed there.
This program - "PT" - is a tool for gathering data that your poker program (e.g. PokerStars.exe) outputs, and compiles statistics based on it. Using PokerStars as an example, you need to go to the Options-menu, select Instant Hand History Options, and click "Save My Hands History". This will make PokerStars save all the hands you've played in text files in the directory specified there. Then, you can point PokerTracker to this directory and it will read the file, and compile the statistics accordingly.
PokerTracker costs $55 to buy, but a trial version (which can read up to 1,000 hands) is available for free. For a long time, PokerTracker was the only program that really filled this role, but a competitor is on the march now, called PokerOffice. I have not used PokerOffice myself though, unfortunately, so I cannot compare.
In conjunction with PokerTracker, there are programs that can pull data from the database that PT creates, and show you statistics about your opponents as you play. Poker is a game of information, and knowing things about your opponents - like how often they raise preflop - gives you a very large edge. Of course, you could keep track of this in your head, but most people find this cumbersome to do with any accuracy better than "little" or "a lot." These heads-up displays (or "HUDs") give you the exact percentage of preflop raises, preflop calls, or most any other information that you may want.
Note: These programs do not tell you what cards your opponents are currently holding. The people that claim they have access to programs that do this are lying.
These programs perform calculations and tell you how well your hand will stand up to your opponents. How often will pocket aces win against JTs? How about 22 vs. a random hand? Etc. When you analyze your play, sometimes these questions need to be answered and you will learn something you didn't expect if you find out. There are many of these programs available, although I like to use PokerStove, mostly because it's free and because of inertia (I started using it, so now I keep on using it).