The term 'expression' in mathematics refers to a combination of symbols that follows certain rules and represents an idea that can be completely abstract or have an equivalent in the tangible world.
We already have a picture of an expression
When an expression finds its place in the 'real world' it can be used to model something, like the velocity of a falling rock or the changes in a population of animals. When this happens, we are trying to 'imitate' what we see in nature with mathematical expressions, and that imitation can be quite precise or not so. It's like trying to sculpt the face of a person, depending on our tools, abilities, and knowledge, we can almost perfectly copy his/her face or not so accurately.
We can use a simple example from physics. A falling object towards the center of the Earth has for its equation:
Where v is its velocity, t is the time, and g a constant.
This is an attempt at modeling that phenomena, and it's more or less accurate depending on whether we consider wind, how distant we are from the center of the Earth, etc.
It's important to notice that math by itself does not pursue that its concepts apply to the so-called 'real world, its ideas can be purely abstract and it's only when we try to use a mathematical expression to describe something that they become 'real'.