Double lugging (or double tapping) is an electrical term that refers to two or more conductors (or “hot wires”) connected to one circuit breaker or for example at the main lug nuts where the service entrance wires are under screw. Generally, these connection points are not designed for the two or more wires to be attached to them and could come loose (a potential fire hazard).
When more than one neutral wire is connected at a single termination point it is a significant problem too as the circuit needs to be isolated. If not isolated, the connection on the other energized circuit would become loose. This loss of neutral under load is a safety hazard.
The correction for double lugging / tapping seems simple enough to accomplish as you need only remove the one of the two wires under screw and attach to its own separate breaker fro example. Unfortunately, this can’t often be done as there are usually no available circuit breakers which caused the double tap to occur in the first place. In this case, connections in junctions boxes outside of the panel may be appropriate. Regardless, its work which a licensed electrician should do and determine what is best under the circumstances.
Do not take your panel cover off your distribution panel if you are not completely aware of how to do it safely and with the power off! Always seek the advise of a professional before starting any work.