Check valves only allow flow in one direction. In the symbol shown flow is allowed from the top to the bottom but only when the pressure is higher than the rating of the spring. Its good practice to write the spring pressure next to the check valve although it's not unusual to have valves without any spring at all and therefore no spring should be shown.
Pilot operated check valves have a small pilot line, shown as a dashed line, that is used to open the check valve and allow flow back through the valve. A common format is the double PO check sandwich plate valve, shown below, that is often used under CETOP directional valves. This allows free flow in both directions when pressure is applied to one side but when the directional valve is closed and no pressure is applied then both check valves close, holding the load in place.
Shuttle valves are most common on load sensing systems. They are designed to always feed the highest pressure to the top connection. The symbol clearly shows that if two different pressures are fed onto the bottom lines then the ball will move either way to allow the maximum pressure onto the top connection.