Notion (noun)

1. An idea or belief, especially a vague or incomplete one.
2. A general understanding or impression of something.
3. A concept or idea.

Origin:

Late middle english: from old french, from latin notio(n-), from noscere "know".

Examples:

1. He had a notion to start his own business.
2. She had a notion that she would like to travel the world.
3. They had a notion that the project would be easy.
4. We had a notion that the company would be successful.
5. I had a notion that it was going to rain today.