If you get it, you'll get it quickly. If not, the explanation might take a few minutes.
The water could have said, "Do you want beer?" which would have made the whole exchange simple. But she said, "Does everyone want beer?" If the first logician did not want beer, she would have said, "No," because each logician is a part of the set called "everyone." The second logician knows that the first one's "I don't know" answer means the first logician does want beer. She wants beer, too, but she still doesn't know the third logician's preference. The third logician knows that the first two would have answered "No" if either of them didn't want beer. And since she wants beer, too, she can confidently say that "everyone" wants beer. Now time to drink up!
You don't have to have a big brain to get it, and not getting it doesn't mean you're small-brained (or any other euphemism). It has more to do with whether you've done this kind of puzzle before. And yes, the three logicians could all be men, but that makes no difference in the joke. This was found in the replies to a Tweet linked by Everlasting Blort. The original source is no longer online.