After a little checking, here was what I found:

There are two companies, GoGo Internet and Row 44, that most airlines are using to provide airplane WiFi service. GoGo Internet uses a ground based cellular data network for data communications and Row 44 uses satellite communications.

Illustrations demonstrating how wi-fi works on a plane can be found here – wlan book

Not very well.

Currently, there is a relatively poor connection which is shared by all people on the plane. This means that the actual speed that you get is lousy.

Welcome to Fluther.

I wish I knew. I barely comprehend how wired Internet service works, and it always gives me the willies when my home WiFi needs rebooting or resetting. I have no idea how even that works.

Then there’s the plane itself: How the hell does it stay aloft?

I like the response from @Bluefreedom. I just wish I understood it…