When you open a faucet, the water pressure in the system drops and the pump turns on. When it builds up full pressure (about 40 psi), it shuts off. If you're not using much water this sounds like a series of short burps, if you're using more water the pump will stay on longer, but will still cycle on and off until you're using the full capacity of the pump. This cycle is normal for the usual pump manufacturers provide. If you upgrade to one of the VSD models, this cycling on and off is eliminated because the pump has a sensor that can turn it part way on if the demand is small.
Steve & Bunny