The original phrase is "The proof of the pudding is in the eating!" Which means you have to eat the pudding to know what's inside of it.
The modern version of "The proof is in the pudding." Implies that there is a lot of evidence that I will not go through at this moment and you should take my word for it, or you could go through all of the evidence yourself.
When ever I hired employees or signed on drivers many would promise the world and really talk themselves up, I always listened but would reply " The Proof is in the Pudding ".
Sometimes they would walk the walk and sometimes they talked a much better game.
If you are the real deal you should not have to oversell yourself, your reputation is what speaks volumes about you, not what you say about you.
And reputations are built one relationship at a time, everyone you meet, everyone you promise something to is building your reputation.
Work hard at delivering what you promise.. it is YOUR reputation at stake.