First, a clarification to the above: Twitter also works just fine with delivery over IM, so any Jabber client like Google Talk (which has a nice client on e.g. Blackberries and works on iPhones et al) will do instead, so no need to use SMS if you don't want to. Plus one can go to one's Twitter page and see a running narrative of everyone being 'followed', so it can be used in a mode with no 'instant' delivery at all.

Which leads to the main point: It's wrong to get hung up on the 'immediacy' of Twitter, because there are other technologies that already do that well (IM, email...), and this is perhaps why I think a lot of people don't get it or dismiss it as pointless. The niche that Twitter fills is asynchronous communication between 2 or more people. It's publish-subscribe.

The problem with all the other forms of instant communication we have (phone calls, SMS message, IM, email...) is that they are all interrupts: people stop whatever they are doing when you initiate communcation this way. But often one just wants to update one's own status, or make an observation about something without causing an interrupt, but still allowing the set of potentially interested people to see your updates when they are available, ready and interested.

Example: Person A is going out to drinks after work with friends. B might join if time permits, but is on a coding deadline and will potentially work rather late. A twitters progress (leaving bar X, moving to Y where there is also food), which does not interrupt B. B reaches a good stopping point, checks A's twitters, is able to meet friends at Y later in evening.

That, and variations thereof, is what Twitter is good at.