Signal Comparisons: "Orthogonal functions"
This is really a mathematics question, you should take a look at Hilbert Spaces for a more detailed answer, but. 

To define a space (e.g., the space of functions) you have to define an inner product between any two elements of the space into the scalars, which must satisfy a few properties, that basically guarantee linearity and uniqueness. This is the generalization of dot product from simple vector spaces, and shares all of its properties. 

For the typical space of functions, the inner product commonly takes the following form (but other forms are possible):

$$ &lt;f(x),g(x)&gt; = \int_{-\infty}^{+\infty}{f(y) g(y) dy } $$

Saying that two functions are orthogonal, just means that their inner product is zero. 

Note that the correlation between two functions is not a function into the scalars (although its zero lag element is). For some definition of inner product, it can be made directly equivalent to the zero lag of the correlation.