Starting a game means you'll start fresh. That means you'll be a level one, you'll have crappy stats, etc. Starting a new game with your current character means everybody in your party will retain their levels. I don't think they'll keep their equipment, but they will keep their levels.
Your main character will retain their equipment as well, though they can't carry over unique items like quest rewards and so forth. Other than that, Amerikranian's explanation pretty much sums it up.
Bear in mind that you have an unlimited number of saved games available, so starting a new game with your current character doesn't mean you can't start a new game from scratch any time you like.
Thank you very much for your descriptive explanation. Sincerely, Vireak