commercial bank
When most people say 'the bank', they mean a commercial bank: the high-street business where you open a checking account, deposit your paycheck, withdraw cash from an ATM, and borrow for a car or a home. It is a private, profit-seeking firm whose core job is to take in deposits from people who have spare money and lend that money out to people and businesses who need it.
Here is the simple machine at the centre of it. A commercial bank accepts deposits, on which it pays little or no interest, and makes loans, on which it charges more interest. The gap between the two — the interest spread — is a main source of its profit; if it pays 1% to depositors and charges 6% to borrowers, it earns roughly 5% on the funds in between. Crucially it does not keep every deposited dollar in the vault. It holds only a fraction as reserves to meet day-to-day withdrawals and lends out the rest, trusting that not everyone will want their cash on the same day. This is fractional-reserve banking, and through it commercial banks actually create new money: when a bank makes a loan, it credits the borrower's account, and that new deposit is fresh spending power that did not exist a moment before.
Commercial banks are the workhorses of the financial system. They channel a nation's savings into productive lending, run the payment system (cards, transfers, cheques) that lets the economy transact, and, by lending, are the source of most of the money supply. Their importance is also their danger: because they lend out deposits, they are vulnerable to bank runs, and because they are so connected, the failure of large banks can ripple across the whole economy — which is why they are tightly regulated and why governments often insure deposits and stand ready to support them.
You deposit $1,000. The bank keeps maybe $100 on hand and lends $900 to a neighbour buying tools. You still see $1,000 in your account and can spend it, while the neighbour now has $900 to spend too — the bank's lending has quietly expanded the spending power circulating in the economy.
A commercial bank holds a fraction of deposits and lends the rest, creating new spending power.
A commercial bank is not the central bank. Commercial banks are private firms serving the public; the central bank is the public authority that serves and oversees the banks. Investment banks (which underwrite securities and advise on deals) are also a different animal, though some firms do both.