Tiger is simply the name for the current OS (operating system). Forget the name and just enjoy it for what it is. Prior to Tiger, there was Jaguar, and before that it was Panther. It's like Microsoft calling their OS Windows 2000, Windows XP, etc. Each new OS is typically a major upgrade. I have a Mac with Tiger and one with Jaguar.
I'm the new owner of a Powerbook G4. I'm very happy I decided to switch. I am just getting used to how OS X is different from XP and other operating systems. I am curious about what exactly this Tiger thing is. I know it's an updated version of something called Jaguar...but what exactly do these things do?