Broker
A broker is the intermediary that gives you market access: it receives your orders, executes or passes them on, and holds your trading account.
A broker provides a platform (MetaTrader, cTrader or its own), prices, order execution and custody of your funds. It earns money from the spread, commission, swaps and sometimes other fees.
There are two main models: the market maker, which takes the other side of your orders, and the agency model (STP, ECN), which passes them on to liquidity providers. Both are legitimate if they are regulated and transparent.
The number one criterion is regulation: check the firm on the regulator's own register, such as the FCA Register in the UK, ASIC's Professional Register in Australia or NFA BASIC in the US, and look at its warning lists. Then come real costs, execution quality and withdrawals.