It always seems Apple renames industry standards to something so that only "Mac people" know what they're on about. Just makes the Mac-PC chasm even wider.
"Airport" is the same system as the 'wireless' system we've got, and you're correct that the Airport Base is what you'd need if you were setting up a network.
If you had a PC, I'd ask if you had a "wireless card" (if it were something you plugged into your laptop), or if it was a built in "wireless adaptor", or a few other things... but you don't have a PC. Regardless, you still need this bit of hardware that is either pre-built into your laptop, or you can slot into it (if Mac's have what's called a PCMCIA port.. a big ugly hole about as wide as a credit card and 7mm thick. Probably not though, because Macs are stylish little things). That thing transmits and receives the radiowaves (microwaves to be precise, I believe) to the "Airport Base", allowing you to have wireless network access.
Best thing you could do is look up a spec sheet for your laptop. Look for anything to do with "airport" (or, "802.11b", or "802.11g", as they're known by the industry standard codes)... or maybe ring up an Apple shop and ask them if you've got one.
Actually there should be (again, if it was a PC, but I'm assuming Apple would) a button which would turn on and off the wireless on your PC if you've got a wireless card built into your laptop (it's there becauise the wireless eats up a lot of battery generally, so when you don't need it you can easily turn it off). Look for that, and if it's there, 90% of the time you'll have an in-built wireless card, so you'll be able to use the wireless at MQ.
Gosh I can crap on. That's what you get for working in an electronics store, I suppose... Sorry!