That the league is recognized by the USBC (United States Bowling Congress), formerly ABC (American Bowling Congress) as a league. The USBC is the sanctioning body in the US. It means that they are the ones that set the rules and make sure they are followed.
In tenpin bowling, the lightest weight bowling ball allowed in sanctioned play is 6 pounds.
The league rules committee.
Sort of. You can have a current sanction card from one league and bowl in another, non-sanctioned league. Your scores in the non-sanctioned league will not be recognized by the USBC, and you will not be eligible for any awards. However, bowling in the non-sanctioned league will not invalidate your USBC sanction, and you will be eligible for any awards earned in a sanctioned league.
A sanctioned league is one recognized by the local affiliate of the ABC with all participating league bowlers in good standing and the league must follow all sanctioning rules.
A league for prisoners
Is it poermissible to get professional instruction during a sancioned bowling league game
Non-sanctioned leagues generally do not have a higher authority that governs rukes.
Most basic fouls would be bowling out of turn, crossing the foul line and using the wrong lane :-)
There is a "yearbook" put out each year. This will contain the averages of all the sanctioned bowlers in your locale. If you do not have access to one, ask your league secretary or the front desk clerk for one. They should have one.
You can view the rules for sanctioned league play in the US at USBC's website at bowl.com.