Consider the space around you. Pick some frame of reference with a fixed origin point in space. To specify an object, you must specify the distance along each independent direction (x, y, and z in 3d space) to arrive at the object from the fixed origin. These independent directions are referred to as a basis for the space. Often these independent bases are perpendicular (or orthogonal).
For higher dimensional spaces its the same idea. It turns out we can even have infinite dimensional spaces whose bases are functions that can be perpendicular in a certain sense. It also turns out that complex exponentials (waves) are an orthogonal basis for a certain space of functions. This is really cool! It means we can refer to any function in this space using the complex exponential basis functions just like we referred to objects in 3d space using three independent directions.
Why is this useful? The magnitude in a particular independent direction in this space tells us about frequency content of that function. So instead of the first coordinate telling you how much x distance there is, it says how much of a certain frequency there is.