We can read for the definition of idea, in the Cambridge dictionary:
a suggestion or plan for doing something:
I've had an idea - why don't we go to the coast?
"Let's go swimming." "That's a good idea!"
If you have any ideas for what I could buy Jack, let me know.
That's when I first had the idea of starting (= planned to start) my own business.
I like the idea of living in the countryside but I'm not sure I'd like the reality.
She's full of bright (= good) ideas.
[ + to infinitive ] It was Kate's idea to hire bikes.
It's not a good idea to drive for hours without a rest.
I think everybody has an idea about what ideas are. Plato's idea is (was?) that they live in some ideal world or space and that they cast shadows in the real material world. We can never have a full picture of these ideas but they can be examined by examining the shadows they cast. We can examine the idea of a circle but we are never able to construct an actual one.
According to Plato mathematics comes close to knowing the ideal ideas ideally. The idea of one of the Platonic geometrical objects (the cube, the tetraheder, etc.) is exactly what they are. A constructed cube is always stained, dusty, or badly formed and is a step from reality. In this respect,
Aristotle thought exactly the opposite. He thought that the idea was a step away from reality, which shows things as they are: muddy, dusty, stained, or stoned. You can try to remove all this from the object at hand and like this an idealized version will appear though this is still an object. It is not something corresponding to an idea in the ideal world.
How is an idea to be viewed? Is it something that really exists, like brain processes? Is it an object that forms the ideal object of another object? Or is it something that exists in a world of ideas only? Are there views different from these of Aristotle or Plato?