If you propose something such as a plan or an idea, you suggest it for people to think about and decide upon.

If you propose to do something, you intend to do it.

If you propose a theory or an explanation, you state that it is possibly or probably true, because it fits in with the evidence that you have considered.

If you propose a motion for debate, or a candidate for election, you begin the debate or the election procedure by formally stating your support for that motion or candidate.

If you propose a toast to someone or something, you ask people to drink a toast to them.

If you propose to someone, or propose marriage to them, you ask them to marry you.