What are the characteristics of an economic model?

During my undergrad economics degree, I never felt that I understood what makes an economic model, and what are the fundamentals of it. The explanations I found (on wikipedia-like sites) are too technical an do not help to create an intuition.

I can think about:

– They find a relationship between two variables (e.g: price and quantity, interest rate and output)

– There must be an equilibrium.

I would appreciate any explanation on what we actually try to do with models and what are their characteristics.