This is one of the hardest questions to answer - because there's not much you can't do with it.
Okay, it probably can't make you some coffee or cook your dinner... but apart from that...
One of the main purposes of the Pandora is gaming. It has dedicated gaming controls (a proper D-Pad and buttons - some things most devices nowadays are missing).
It is powerful enough to emulate Amiga 500 games in fullspeed so you can relive your past. Of course, older computers like the C64, the MSX, the Atari ST, the Spectrum, etc. can also be emulated with ease.
It can also emulate classic video game consoles up to (and including) the 32bit generation - and even some 64bit consoles!
Another way to relive your past is by using rewritten game engines. That way, you can play games like Ultima VII, Baldur's Gate, basically all classic Point-and-Click Adventure games, classic Text adventure games, etc.
But there's more than just retrogaming:
Thanks to the growing Linux community, there are great games like Battle for Wesnoth, FreeCiv or NumptyPhysics.
And there are also a lot of homebrew developers, releasing games like Panjoust, Gianas Return or Pandora Panic.
You can check out the appstore what's available already - and this is only the beginning, as the Pandora is just out for a few weeks...
The Pandora features an Open GL ES 2.1 compatible 3D chip - so be prepared for some fast, hires 3D-possibilities.
Playing is nice, but sometimes you want to check your eMails, surf the web for some news or use IRC, MSN or ICQ to chitchat a bit.
No problem - you can do so with the Pandora using WiFi, Bluetooth or a modem.
What's your favourite browser? You can use FireFox, Chromium, Arora, Midori, .... or, if you rather like the kinetic scrolling browsers for mobile devices: Fennec.
It's up to you.
The Pandora offers a complete desktop mode. That does mean: Windows, a start menu, multitasking. You can run multiple programs at once.
You can write some text in an office application while listening to music or following an internet chat. It's just like a PC. Only smaller. And more portable.
Developing for the Pandora is pretty straightforward: As it features a standard Linux environment including an X-Server, you can port apps and games pretty fast. Most work by simple recompiling them.
And if you want to develop on-the-go: You can install development tools and IDEs like CODE::BLOCKS onto the Pandora - and code, compile and debug directly on the machine!
Is this it?
No. This is just the beginning. The top of the icing. You can use USB devices with the Pandora as well.
Want GPS? Connect a receiver. There is Linux GPS Software available.
Want to use a proper mouse and keyboard? Simply connect them using an USB hub. Combined with the TV Out cable, you can basically turn your Pandora into a small desktop PC.
There is so much you can do. You could connect a MIDI device and program or play your synthesizers from the Pandora.
You could connect an USB harddrive and use it as mini-Webserver. Or Fileserver.
The possibilities are endless - you just have to imagine it.