In most cases, the debtor's discharge is issued 60 or more days after the original date of the meeting of creditors. Note that a debtor's discharge ("fresh start") is not the same event as the closing of the case. The discharge is the order which releases individual debtors from personal liability for most debts and prevents creditors from attempting to collect those debts in the future.
Not all debts are discharged in a bankruptcy. For example, some debts are deemed "non-dischargeable" by law. In addition, the trustee can ask the court to delay, deny or revoke (undo) a discharge in appropriate circumstances, and a creditor can ask the court not to discharge a particular debt. Because a chapter 7 discharge is subject to many exceptions, debtors and creditors should consult a lawyer to determine which debts have been or will be discharged.
Shortly after the meeting of creditors, the trustee will determine if there are assets for her to administer. Regardless of the type of case it is, the case remains open until the court closes the case, and the debtor has an ongoing obligation to cooperate with the trustee so long as the case is open. The order of discharge does not affect this obligation to cooperate.
If the trustee determines there are no assets to distribute to creditors (because all assets are exempt or liened), the trustee will file a "no asset" report. Approximately 90% of chapter 7 cases involving individual debtors are no asset cases. In a no asset case, the court generally closes the case approximately 45 days after the discharge is entered, unless there is ongoing litigation or some other matter which keeps the case open.
If the case trustee determines that there may be assets for the trustee to administer, the case will be considered an "asset case." It is usually 1-3 years before the typical asset case is fully administered by the trustee and closed by the court. Additional information regarding asset cases is available here.