The user decides if he wants to accept or reject the quote. There are 3 ways to accept/reject the quote. Below you see a list of examples:
From the PDF, if you enabled the Accept and Reject fields:
Inside the quote on My Account page:
If the user accepts the quote he will be redirected to the Checkout page to complete the order.
If the user rejects the quote, the order status changes to Rejected quote and it is no longer possible to re-open the quote.