In an election or other voting situation, "winning by a landslide" means winning by getting a lot more votes than the other sides. The number of votes that constitute a "landslide" depends on the situation.
A "landslide" is what happens when rocks or dirt roll down the side of a mountain and cover things up. The phrase "win by a landslide" comes from this idea. You can imagine someone getting so many votes that the votes cover them up.
The opposite of "winning by a landslide" is "just barely winning" or "winning by a tiny margin".