Hey Dentaldream,
The PDAs basically started out as personal organizers-- An electronic appointment book, phone/address book, note pad, calculator, etc. all in one. There were pocket electronic organizers before, but they were clunky with supertiny keypads. Apple tried to introduce a new stylus-based one (the Newton) back in the early '90s but it bombed-- The handwriting recognition did not work very well.
The stylus-based PDAs really took off when USRobotics introduced the PalmPilot (USR was eventually bought out by 3Com, then the division was spun off as Palm Computing). It works because USR simplified the handwriting recognition-- Rather than trying to recognize any handwriting, it needs the user to learn to write a certain way (the "Grafitti" system). What made it even more attractive is that you can actually exchange information and programs with your PC ("hotsync"). None of the previous PDAs could do that.
After the Palmpilots came out, they started adding more and more stuff to it-- Like combining it with a cellphone, which makes sense because you have the phone/address book in there already. There are also newer ones with a GPS receiver built-in to give you a moving-map display, and others with things like cameras and WiFi functionality (Bluetooth or 802.11) so you can send and receive email from one if you are within range/have access to a wireless network, and even MP3 player functionality for the health nuts who need to listen to music while they work out.
I bought the Palmpilot when it first came out because I was tired of jotting down info and reminders on little scraps of paper and Post-It notes that gets lost. Just getting rid of that mess of little slips of paper was worth it to me.
These days, the biggest use I have for it is definitely the drug and medical consult databases. But it's also great for keeping contact information (phone numbers, addresses, email addresses, etc.) of your friends, colleagues, patients, you name it. The calculator comes in handy too when you have to calculate concentrations and milligram quantities of lidocaine and epi that you administered.
I've had my Sony Clie SJ30 for a while now (2 years) but you can get one with better specs these days for around $200, like Gavin's Tungsten E or my classmate's Clie TJ35. If you want one with a cellphone like the Samsung SPH-i330, expect to spend $400+. The really fancy ones can cost all the way up to $1000+.