If something's wobbly, it has a tendency to sway or lurch from side to side, like the wobbly wheel on a broken tricycle or the wobbly legs of a cruise ship passenger who has just set foot on solid ground after a week at sea.
If your chair is wobbly, you may need to tighten the legs with a screwdriver. And if you're feeling wobbly during gym class, you probably need to sit down and drink some water. Anything or anyone that wobbles can be described as wobbly, and both words come from a root meaning "to weave back and forth." When the word is capitalized, it's a nickname for a member of the labor union called International Workers of the World.