Convincing means strong enough to make people believe it. The argument holds, and so does the performance.
It describes evidence, arguments and acting, so a convincing case, a convincing explanation and a convincing performance all mean the same thing from different angles. Sport uses it for margins, and a convincing win is a comfortable one. The negative is where the word does its best work in British English, since not entirely convincing is a devastating thing to say politely. The verb is convince and the state is being convinced.
1adjectiveconvincingAble to make someone believe something is true or genuine.
“It was not a convincing explanation.”
2adjectiveclearClear and decisive, of a victory.
“They had a convincing win at home.”