Bankruptcy is a process where individuals and companies can end or attempt to pay off some or the entirety of debts with protection by the Federal Bankruptcy Court. Bankruptcies are typically either of two possible types: liquidation or reorganization.
"Chapter 7" bankruptcy is associated with the liquidation type of bankruptcy. It's called "liquidation" because the party (trustee) handling the bankruptcy may take and sell (liquidate) some of a person's property to pay off some of that person's debt. Property that cannot be sold (exempt), is determined by state law.
"Chapter 13" bankruptcy is usually associated with the reorganization type of bankruptcy, which is most commonly used by individuals. In Chapter 13 bankruptcy, persons keep all property, but must pay monthly installments in 3 - 5 years to repay a negotiated amount of debt.