Hi there,
Yep, you're right. "Home Theater" is all to do with TV, five to seven "main" speakers and a sub, all in one room. Like you said, you don't care about TV, so just ignore all the home theater talk.
What you're describing is a multi-zone system, I think. You have three zones -- basement, main room and outdoors. You'll need a source for the audio programming, which I assume you have. You know, something to play CDs, records, radio and so on.
If you've already picked out a receiver and speakers, that's a great start. Again, assuming you already have your "source" (CD, radio, whatever), then you're close to done.
From here, you'll need everything to connect it together. In general, if you're not already wired from the point where your receiver will be to all the locations where you want your speakers to be, you'll have to get that set up. It's not too hard, but it'll take a little effort.
Now, in each of these "zones," would you like to be able to control the program material played? That is, would you like to be able to listen to a CD outdoors, while someone else listens to the radio in the basement, and have everything be controlled from a single receiver? If so, you'll really need a two-zone receiver (at least). If you want to control three zones independently at a time, you'll need a three-zone receiver. Two-zones receivers are pretty common while three-zone receivers are harder to come by -- but they certainly exist.
If you always want to play the same thing in all zones, things are simplified slightly...
How do you want to control volume to each zone? For example, if you're listening at a lively volume in the basement, you may not want the same thing blaring on your outdoor speakers. The multi-zone receivers can control volume individually for each zone, so that's one way. For my outdoor speakers, I also have a volume knob set in the wall so that I can control it right there.
One other thing to think about when controlling volume via the receiver's multi-zone capabilities is that you generally have to be able to hit it with an infrared based remote control. That means that if you want to remotely control from the basement, you'd have to go upstairs and point the remote at the receiver, then go back downstairs, etc. Kind of a pain. Again, you can get around this if you have volume knobs in the basement, but you can also get around it by getting a universal, programmable RF-based remote. With a remote like that, you can use it anywhere throughout the house to control your system without being "line of sight" to your receiver.
As suggested by stratman, the Sonos system is pretty cool. That will give you control over your source material, assuming it's on a PC (or perhaps a NAS). You would be able to control volume from it as well, but I think it would be applied to all zones, unless you buy multiple Sonos boxes or remotes. IIRC, the basic Sonos system (the box and one remote) is about $700 or $800. It's cool for sure!
Yeah, it gets complicated, but it's not all that bad. I'm sure you can get it going, and your husband will really appreciate it!