A bylaw is a rule that a group or company sets up, one that all members or employees are meant to follow. The bylaws of your school's student council might stipulate that all student council officers have to be in good academic standing.
In Britain and some other countries, a bylaw is a local law, rather than a national one: "The city's bylaws don't allow me to sell my artwork without a special permit." In the U.S., bylaws apply to organizations rather than cities, towns, or states. A club's bylaws, for example, might state that each member has to pay a small membership fee. Bylaw is rooted in the Old Norse bi-lagu, "town law."