What is the meaning of inspire?

It comes from the same root as "spirit". If you expire, which is Word also containing that root, your spirit leaves you and you die. "Inspire" means that a spirit has entered you: the spirit of God or a muse. Saints or others who suddenly felt filled with a spirit which came from without claimed that they were "inspired" by that spirit.

That is the literal meaning of the term. We do not now usually think about benevolent spirits taking people over. The Word is used to describe being filled with enthusiasm for something from an external cause. It is usually a good enthusiasm: people talk about being inspired by the speeches of Churchill but hypnotized by the speeches of Hitler.