Question about web security

Wanted to put out a question to readers. I recently happened to tune in to the Kim Komando show and heard something that sounded like a mistake. However, I'm not a security expert, so I'd like to find out more.

A caller had been making use of his neighbor's unsecured wireless connection when his own internet was down. He was wondering about the security hazards of doing this.

Kim's answer was mostly correct, which was to say that anything you transmit or receive over the web is visible across the entire network. By using freely available software, your neighbor could potentially steal your information. He could have a packet sniffer and log the information on his computer, or even in the router.

Kim then went on to say "So obviously you wouldn't want to do any banking over the unsecured line, because you don't know who's looking at your data."

These struck me as solid words of caution, but potentially incomplete. Presumably your bank would make you log in over an SSL connection. My own understanding is fuzzy, but I believe this means that the data gets encrypted at each end before being sent over the network, and only your client and their server have the information necessary to decrypt the data.

Can anybody confirm or deny that my understanding is correct? Is there some way you know of where the neighbor could read your secure data as plain text? If not, what information is your neighbor lacking that would allow him to see it?