http://www.phrases.org.uk/meanings/proof-of-the-pudding.html
'The proof of the pudding' is just shorthand for 'the proof of the pudding is in the eating'. That longer version makes sense at least, whereas the shortened version really doesn't mean anything - nor does the often-quoted incorrect variation 'the proof is in the pudding'. The continued use of that meaningless version is no doubt bolstered by the fact that the correct version isn't at all easy to understand.
The meaning become clear when you know that 'proof' here is a verb meaning 'test'. The more common meaning of 'proof' in our day and age is the noun meaning 'the evidence that demonstrates a truth' - as in a mathematical or legal proof. The verb form meaning 'to test' is less often used these days, although it does survive in several commonly used phrases: 'the exception that proves the rule', 'proof-read', 'proving-ground', etc. When bakers 'prove' yeast they are letting it stand in warm water for a time, to determine that it is active. Clearly, the distinction between these two forms of the word was originally quite slight and the proof in a 'showing to be true' sense is merely the successful outcome of a test of whether a proposition is correct or not.
As an addendum, now I really want some pudding.