It may seem like a silly question, but the definition of what a bank is can vary quite dramatically. The common definition in this instance is:
"[A] business establishment in which money is kept for saving or commercial purposes or is invested, supplied for loans, or exchanged, or the offices or building in which such an establishment is located."
or
"a financial institution that accepts deposits and channels the money into lending activities." (Wordnet™ 1.6, - 1997 Princeton University)
Banks are distinct from Building Societies in that they are commercial organisations whose primary purpose is to make money through the business of providing financial services, whereas a Building Society is chiefly a Savings and Loans association.
What is a Building Society?
Building Societies are similar to banks in that they provide a wide range of financial services, including personal banking, credit cards, loans and so on. However government legislation states that 75% of a building society's total business must be devoted to residential mortgage loans and related products, such as home equity loans, whereas a bank is under no restrictions as to the mix of its financial business.