Napoleon did enter Moscow, but he found it somewhat abandoned. While his army went absolutely mad in pillaging, there was no Russian surrender, against his expectations.
The story goes that wise old Kutuzov had decided after the bloodbath at Borodino to engage in a strategic retreat - to give up Moscow in order to save the Russian army. He considered that a battle for Moscow against Napoleon might risk the destruction of the Russian army, and therefore result in conquest. Better to cede some territory, draw back and regroup, then watch, wait, and plan for a more opportune moment to engage.
I think we've seen this a number of times in the SMO, too - ceding space in exchange for time. I think Big Serge put it that way if I remember correctly. We've also seen how the ceding of space or strategic retreat can really shake people up because it looks like a defeat, or cowardice, etc.
Below is a documentary about the events leading up to and including Napoleon's downfall in Russia. I haven't seen the whole thing yet. This is where the quote above comes from. It's a long doc, but the historian seems like quite the excellent dude who has a crack production team. There's good graphics & maps show troop movements and battle layouts, fitting music, a number of historical paintings to provide some real colourful context, and also quotations from officers. Altogether it gives one a certain sense of the gore, the starvation and the cold, and the misery and suffering of the whole thing, the way wars are begun and extended and ended ie. negotiated politically.