Within a speaker different drivers handle different frequency ranges. A two way speaker has different drivers handling two frequency ranges; in this case a woofer for the low freqs and a tweeter for the high freqs. A 3 way speaker also has a midrange to handle the middle frequencies.
A couple of notes:
1. If a speaker has multiple drivers handling a frequency range, that doesn't change they type of speaker. For instance if it has two woofers and one tweeter it's still a two way speaker.
2. Don't let anyone convince you that more is better. There are many two way speakers that are better than three way speakers. In fact, for a given price a manufacturer can put two higher quality drivers in or three lower quality drivers. Go by what sounds best, not how many drivers are in the box.
3. There are also four way (and I'm guessing higher) speakers.