When something is convincing, it makes people agree with what it claims to be true. Describe an argument as convincing if it wins you over and makes you believe in its rightness.
To figure out what convincing means, remember that vincere is the Latin word for "to conquer." Add on the prefix con-, meaning "with," and you get something that has the ability to conquer — whether it's doubts, disbelief, or hostility. The suffix -ing tells you that the word describes the action or result of something. The result of a convincing argument is more people who have joined your side or cause.
adj causing one to believe the truth of something
appearing to merit belief or acceptance
freeing from illusion or false belief
intended or having the power to induce action or belief