A pipe that burst
A half-inch supply line under normal residential pressure moves several gallons a minute. The difference between finding it in ten minutes and finding it in four hours is the difference between a wet wall and a rebuilt floor.
The main shut-off, before anything else
In most New Jersey basements the main shut-off is on the street side of the foundation wall, near where the service enters, usually within a few feet of the meter. It is worth knowing where it is before you need it, and worth turning it once a year so it does not seize.
If the valve will not close, the curb stop in the street can be shut by the water utility. That call is worth making immediately rather than after twenty minutes of trying.
Why the wall gets opened even after it stops
Water inside a wall cavity has nowhere to evaporate to. Insulation holds it, the bottom plate wicks it, and the cavity stays at high humidity for weeks. Closing the wall back up over wet framing is how a plumbing repair becomes a mould problem three months later.