In banking or brokerages, loans and credit extended are assets as they're value owed to the bank by others. Deposits, held certificates (e.g., stocks), or stored valuables (gold in a safety deposit box) are liabilities because others can make claims on them.

Checking accounts are literally "demand deposits" in the sense that the funds are demandable at any time by the accountholder. Many savings accounts actually have limits on the amount or rate of withdrawal. These are typically large and generous, but they may exist.