In a dream world, I guess it would be a portable, reliable, versatile device that gives the user instant access to data, communications, and productivity resources.
I don't know exactly what a handheld/mobile device is in the "real world" as I hope to explain below. Maybe the way to do it is to figure out what a handheld/mobile device isn't and then write a definition from what is left over

Portability-my handheld is portable. However so is my laptop, unless I need the disk and DVD drives, spare battery, power cable, ... you get the picture. Then I have to drag a bag w/ me that might as well contain a dozen bricks for all that it weighs. With the increase in abilities of handhelds (built-in wi-fi & bluetooth, keyboards, cameras, science probes, gps, VGA screens, etc) I am beginning to feel as though I have two laptops! I can't seem to keep a battery charge to run all of these fantastic items and still avoid plugging in throughout the day. So much for mobility (unless you count the 5 feet I can walk with my powercord attached).
Reliability-my handheld is reliable. Unless all of the items I listed above suck the life out of my battery and it dumps my info.
Versatile-my handheld is versatile. There are tons of applications out there that will allow a user to do just about anything they wish. Unless I want to share information with someone who is using a device with a dissimilar OS (and I don't own a "translating" program). When there is some form of "union" between OS's for data transfer, then there will be versatility.