So, I do not know the source, but I do know what it means.
qui cupit, capit omnia
He who wants, takes all things
You are pretty much correct on the more metaphorical meaning, as it is trying (in my opinion) to convey that if you want something (and presumably work for it), you can accomplish anything you want. The qui is a relative pronoun, and the cupit, capit is most likely an intentional choice to bring together the alliterating elements and make it sound nice.
If anyone knows the source, that would be greatly appreciated.
I found the source! It appears to have come from a book by John Amos Comenius called Janua Linguarum Reserata. This was a Latin textbook for learning the language (as far as I can tell) and the quote itself can be found here. The English translation found in this copy reverses the clause order:
He conceiveth [catcheth] all things, who desireth to do it.
The quote actually continues:
Etiam quae prima aggressione captum superant.
Even those things which at the first undertaking go beyond his reach or capacity.
This again implies the sense of "he who sets his mind to it can accomplish anything." Rather inspiration, I would think!