Im assuming you are talking about a coaxial speaker. A 4 way usually has a mid woofer, mid range, tweeter and super tweeter, a three way may have a mid woofer, mid range, tweeter.
Honestly with every coaxial I have ever dealt with once you get over 3 way you are just wasting your money. Most two ways sound as good if not better then 3 or 4 ways.
Once they start adding multiple tweeters and super tweeters the high frequencies sound harsh.
Ok, a 1 way speaker is like a subwoofer. It only has one speaker. Take a door speaker for example that has the main speaker and adds a tweeter on top, that's a two way. A 6x9 speaker that has all sorts of little speakers with it will be more. So, If you have a main speaker with a bunch of little speakers on it you just add all of them with the main speaker and you will have how many "way" the speaker is. I.E. A 6" by 9" speaker that has three other speakers on top kinda of the main speaker would be a four way speaker. It gives you many different frequency levels of your music through one speaker. Don't be fooled though, with a good enough speaker you don't need a "thousand way" speaker. It's all in the quality (cost) of the speaker.