I don't claim to know all about banking. But here is a start.
Front office, the revenue generators, the ones who bring in money:
Investment banker - Initial Public Offering (IPO), Mergers and Acquisition (M&A), Debt Capital Markets ( DCM).
Traders, they create the markets, giving out a bid and ask for securities. Usually, they're defined by asset classes - equities, fixed income, currencies, commodities.
Sales, they take the price quoted by the traders and attempt to transact with counterparties, such as hedge funds, pension funds, real money.
Research, the guys who look into the markets and publish reports and newsletters to be circulated to the bank's clients.
Middle office, the one who support those above:
Risk management, watches the bank's risk limits.
Research, some consider to be middle office.
Back office, the guys who come in to book keep all the action:
Operations, when a deal or trade is done, these guys come in to log all the statements and make sure everything is squared off. Whatever security is bought, it needs to be matched off with a corresponding ticket.
Compliance, they ensure whatever is going on in the bank meets the requirements set by
MAS.