An exchange is a service, usually a website, where users can trade their assets. Sometimes these trades are completed by matching open "buy" orders to open "sell" orders, and sometimes this is done by a service for a predetermined price.
For example, you can use an exchange to trade your Bitcoin (BTC) for Litecoin (LTC), or vice versa. On some exchanges, you can exchange cryptocurrency for fiat currencies; for example, trading your US dollars (USD) for Bitcoin (BTC).
Often you will be restricted to opening a single account on each exchange. Most exchanges will provide you with at least one wallet for each cryptocurrency that you want to use on the exchange.
There are dozens of exchanges, each with their own website, interface, regulations and availability. Using CryptFolio, you can manage a wide range of exchange accounts – check out CryptFolio's list of supported exchanges.
For more information, check out these resources: