Fundamentally, a bank is a business that holds onto your money for you and uses it to create profits by investing that money or loaning it out to other customers. Most banking practices as we know them can be traced back to antiquity. The oldest bank in the world is the Monte dei Paschi di Siena, in Italy, which has been operating continuously since 1472.
When you make a deposit or buy a savings product, you're essentially loaning money to the bank. It pays you back in interest for that loan, but rates can vary widely depending on the bank and the way you're putting money in. Banks then lend that money to other customers and invest it, which is how they make their money. (Well, that and your ATM fees!)
A bank is a business like any other: run for profit, by people who answer to their investors. The more money they make for their investors, the happier they are. This means that all activities the bank engages in are expected to show a profit. Like any company, successful management of a bank means finding the best balance between customer care and profit. It wants your money, but you don't want the bank to have it; you want the best interest for your deposits, but the bank wants to recoup that money any way it can. Because the global market changes so fast these days, the balance is trickier to find than ever. Often, customers pay the price.
Advertising, lobbying and risk assessment are the key expenditures banks must pay in order to stay on top of the competition. Advertising, of course, is essential to making us believe one particular bank is the best so that we will loan that bank our money. Lobbying, to make sure that governmental regulations don't harm their profit margin or executive salaries, may mean a more competitive and innovative business environment. And risk assessment is the science of making sure that a bank's loans and investments don't turn around on them and harm the bottom line.