I didn't really understand the point of tablets until I used one extensively for testing a particular application at work, and got used to being able to view my calendar and inbox without the compromise of a phone-sized screen anywhere in the office.
Like Jobs supposedly said, when they're made properly, they're intentionally a class that sits in-between "smart phone" and "laptop". They're not intended to do everything either of those device types can do, just like those devices can't do everything (well) that a tablet can.
Right now, I mainly use mine as an electronic replacement for paper documents.
I can take notes using a stylus, which is a lot more conducive to a conversation than pecking away on a laptop, and because they're electronic/backed-up, I don't need to worry about losing the one notebook that contains what I'm working on.
I can view my calendar anywhere, and unlike a printout it's updated in realtime. I can view my work email. I could do those last two things on my phone if I really wanted to, but the having a comfortably-sized display is much nicer.
I can read electronic copies of documents instead of relying on printouts that may be outdated.
Because it's a tablet, I don't need to sit down to use it like I would with a laptop.
All of the other things it can do (RDP/SSH to systems I'm responsible for) are a great benefit as well, but it's the replacement-for-printed/handwritten-materials aspect that I find most useful about it.
Much to my own surprise (I'm not a big fan of Apple, traditionally), I went with an iPad, because it really does have that "it just works" quality. My paper-and-pen notebook or physical printouts never crashed or took five minutes to boot up, and neither should the thing that replaces them.
I have an Android phone, and when something goes wrong with it, it literally does take multiple minutes to reboot. That's just ridiculous.
I've seen the tablet editions of Windows, and it's painfully obvious that Microsoft's staff still haven't learned anything about making a UI that takes advantage of a particular form factor, as opposed to trying to make one UI that tries to do everything and then attempt to use that on all device types.