Every time someone submits the contact form on your website, a new deal is created inside Funnel, and a notification email is sent to both you and the sender.
You can view deals as your potential deals, stored outside of your inbox. The benefit of this is that it lowers the risk of you forgetting to follow up or reply to a customer just because newer email has piled up on top of the one you're supposed to work on. Funnel also provides you with many other conveniences and tools that you can use to manage and track your deals.
Since Funnel is connected to your Gmail account, you can reply to these notifications and the message will get delivered to both your customer, and Funnel so you can view the complete conversation no matter where you send the reply from. (NOTE: Funnel can't access your inbox, or read your existing messages.)
Deals are not limited to a single contact. You can add people from your contacts, or by simply CC-ing them to the email thread, and they can opt out of the conversation at any point as well.
You can delete any deal within your Funnel account. If you decide to delete a deal, only the deal within Funnel itself will be deleted, not the message thread that may exist in your inbox, since Funnel doesn't have access to your inbox.
The contact that resides in your contacts database will remain intact, and the contact information, along with all the messages you may have had within the deal will remain in your Gmail or Google Apps account.