New Game+ will start creating separate saves just like your current game has been doing. Autosaves and quicksaves will eventually be overwritten but manuals won't unless you choose to save over an old save.
You can also import a Witcher 2 save, or simulate one, just like you could when starting your first game.
You'll start the game from the beginning, but with the Geralt you have in the save you start NG+ from. You'll keep all the items you currently have except quest items, crafting recipes (you'll find new versions with higher level requirements), books, trophies, and gwent cards.
The world (enemies, quests, equipment level requirements) will be levelled according to your Geralt's level; if you start NG+ at level 50 the first ghouls will be level 51 or so. That's the main difficulty in NG+: everything deals a lot of damage compared to starting at level 1. But Geralt also starts off stronger and with whatever skills you picked for him in your first game.
I think that covers the basics. There's a lot of info available around the web, too.