In nautical terms, the term "leeward" means the side that is downwind of something else. So if you are to my leeward, I am between you and the direction the wind is coming from. In that case, I am to your windward side -- that's the opposite of leeward.
It makes sense for the men to tell Huck to keep the raft to their leeward side because the men think that there is disease on the raft. So they want it to be downwind from them so that the germs cannot blow from the raft to them.