What it means
Means winning by a massive margin so the other side get absolutely buried. You hear it a lot in elections, sport, quizzes, polls, pretty much anywhere there's a score and one side romps it. It's standard everyday English, especially in the UK, for a result that wasn't even close.
Usage examples
"Played darts down the local and Dave won by a landslide. I clipped the wall twice, Baz nearly speared the dog, and Gaz still wanted a rematch."
"Their candidate won by a landslide, taking nearly every seat."
"We won the pub quiz by a landslide, the others didn't stand a chance."
"City won by a landslide, mate. By half-time their lot already looked like they'd accepted their spiritual eviction."
"She won the student election by a landslide, not even tight. The group chat was basically just everyone posting shocked faces and calling it early."
Where it comes from
It comes from landslide in the literal sense, when a huge mass of earth or rock slides downhill and overwhelms what's below. That image got borrowed into politics in the late 1800s for a victory so one-sided it sweeps the opposition away, then spread into general use.