Unlike the stock market the forex market is decentralized. There are no central exchanges but computer networks in which orders are executed between all market participants, brokers, institutions or retail traders. In that sense it is an over the counter market (OTC). The facilitation of orders is being made via large banks or forex brokers which are the main providers of liquidity.

It is opened 24 hours per day five days a week, because when a market is closing then another one is opening and can execute the orders of investors/traders. In forex trading there are five major markets:

London from 3:00 am to 12:00 EST 

New York from 8:00 am to 5:00 pm EST

Sydney from 5:00 pm to 2:00 am EST

Tokyo from 7:00 pm to 4:00 am EST

Singapore from 9:00 pm to 5:00 am EST

So someone can theoretically trading 24 hours per day and some sessions are also overlap.