When your washer discharges used water, that water goes down a drain. As the water moves into the drain, it creates a suction effect in the pipes. If your washer isn't properly vented, you may hear gurgling or slurping noises coming from other plumbing fixture, such as a nearby kitchen or bathroom sink. This is because the suction caused by the discharging water is pulling in air from another part of the plumbing system in order to equalize the pressure.
In order to prevent gurgling or sucking noises coming from sinks, both the sink and the washer should have air vents that allow air to flow into the system when either the sink or the washer is draining. In some older homes, especially those built before electric washing machines came into use, the system may not have an air vent that serves the washer. A plumbing professional can inspect your water line to determine whether the noise is caused by a bad or missing vent.
In some situations, the air vent that allows your washer to drain properly may be blocked or the drain pipe itself may be clogged. A clogged washer drain is likely to lead to water remaining in the machine or draining very slowly, which may also cause the gurgling noise. Clogged washing machine drains can be caused by a piece of clothing, such as a sock, getting into the outer tub and impeding the pump from emptying the tub water. Removing the obstruction should solve the clog issue.
Gurgling noises in your sink as the washer drains are usually signs that the air venting system is not functioning properly. They may also be a sign that there is a larger problem with your plumbing system, especially if you have a septic tanks system. Talking to an experienced plumbing professional is your best choice when facing a problem you're not comfortable handling yourself.