Following is a list of features and specific "cool things" I think you can point out if you are trying to explain to a friend why they should upgrade.
For the record, I installed Leopard on a 1.24 GHz iBook G4, and it runs beautifully, which in itself is a selling point.
1. Finally, a Record button for your actions
Automator now has a UI recorder. Anyone who remembers the good old days of macro recorders before OS 8 will look at this and sigh, but I, for one, welcome my new robot overlord. Automator is finally useful for mortals with UI recording. Oh sure, it isn't perfect, but it really beats trying to explain just the concept of Automator to the average human. Never mind the metaphors and the workflow within Automator itself -- eyes will glaze over. UI recording is absolute heaven when you do a lot of drudge work, like contracts, filling, prepping photos, etc.
2. Mail gets GTD fever
If power users turn up their noses at Stationary in Mail, point out how they can now put their notes, to-do's and RSS into Mail. I haven't really set all this up as I'd like yet (the iBook isn't my primary work machine), but my unfettered hatred of Mail.app is somewhat lessened now by the fact that it is starting to behave like a "real" email client. The notes and to-do's are icing on the cake, but also very important if you like to get things done and stay organized. A few smart folders and you have a truly powerful system. Still, it is disappointing to see Apple take half a decade to figure out the whole "archive mailbox" thing, but pobody's nerfect I guess.
3. Web clipping makes Dashboard relevant again
My wife quit using Dashboard long ago. It simply served no purpose for her. But web clipping, baked right in to Safari? That had her mildly interested. Tracking the top 3 Twitters, or whatever the top story on Perez or TMZ happens to be with a keystroke is a selling point for folks who aren't using RSS. The only downside is that you need a pretty big screen if you want more than a couple of pages to appear.
4. Shared drives finally "just work" and Shared Screens work with other OS'es
Granted, there have been issues with networking in Leopard, but seeing shared Macs in my sidebar? That's pretty sweet. In previous versions of OS X you had to click on Network, now it just shows up. Is a few clicks a big deal? Well, for the average user, yes, this is a big deal. The average user doesn't like to explore. They can be timid, and frankly, don't necessarily know (or care) what the Network thing even is. Displaying networked components directly in Finder will greatly increase the probability that users will at least see everything. It has already saved me time when trying to reconnect and move things around my home LAN. For me, the real fun was seeing how VNC "just worked" when I was able to access my Mac mini (which was already running as a VNC server) via Screen Sharing. Even though the mini runs Tiger, and despite a slightly wonky connection, overall it was super easy to set-up. Think about it another way: average users don't want to run a third-party application like Chicken of the VNC. Average users don't necessarily trust those apps (thank you, Bonzi Buddy) and it is a lot easier to remotely control a machine if the functionality is built into the OS. Oh, and did I mention you can share screens with Linux? I finally have a use for that old Dell laptop and my Ubuntu CD!