Differential problems should be checked out as soon as possible. Symptoms include clunking when you accelerate or shift between drive and reverse, or a high-pitched howling type of noise.
An axle connects the two wheels on opposite sides of the vehicle. The differential refers to the gears and bearings either inside the transmission or the housing of the axle.
The differential lube level should be checked with every oil change. Some differentials require periodic cleaning and repacking of wheel bearings. If you drive an SUV or light truck, and especially if you pull a boat (meaning these components may get submerged in water), axle lube should be changed every year. Please refer to your owner's manual for factory recommended maintenance intervals for your specific vehicle.