Full-reserve banking is a banking practice in which the full amount of each depositor's funds are available in reserve at all times.
This system is largely non-existent in the current global landscape and hasn't been since the early 1800's. What this exactly means is that if a bank had total deposits of $1000, they would lend out $0 and keep all $1000 in its vault until such time that the depositor wanted to reclaim it. This is in direct contrast to fractional reserve banking in which only a fraction of the deposit stays in the vault and most of the deposit is lent out.
In a full reserve system banks make money by charging its depositors a fee to keep their money and to provide services such as transfers and payments. The way that lending would occur in such a system would be for banks and other financial institutions to offer separate options for those who want to invest their money or allow it to be loaned out at interest.
This can be done with such vehicles as Certificates of Deposit. The system works by taking money that the depositor may not need for some period of time and using it for a profit centered venture. The depositor and the financial institution would share a level of risk associated with the venture but in exchange would also share in its gain.
This type of system is far more fundamentally sound and does not create the types of credit bubbles, systemic risk or too big to fail scenarios that occur in fractional reserve banking. It also eliminates the need for a central bank or a lender of last resort. This system does not eliminate lending, but rather creates a more stable and long term view of lending. Banking and investing become two different and separate services, one with no risk and no gain, and one with risk and the potential for gain.