What does it mean for two functions to be "orthogonal"? then, give a specific example of two orthogonal functions.

Ihave often come across the concept of orthogonality and orthogonal functions e.g in fourier series the basis functions are cos and sine, and they are orthogonal. for vectors being orthogonal means that they are actually perpendicular such that their dot product is zero. however, i am not sure how sine and cosine are actually orthogonal. they are 90 out of phase, but there must be a different reason why they are considered orthogonal. what is that reason? does being orthognal really have something to do with geometry i.e 90 degree angels?
why do we want to have orthogonal things so often in maths? especially with transforms like fourier transform, we want to have orthogonal basis. what does that even mean? is there something magical about things being orthogonal?