An infringement is a minor offense that involves breaking a rule or a law. If your sister takes a chapter from your book and publishes it as her own, you could sue her for copyright infringement.
An infringement can result in legal penalties if you’re breaking a law, as in the case of a copyright infringement or a patent infringement. An infringement can also be a violation of a rule or an agreement that applies in a specific situation. In that case there are no legal consequences, but there are still penalties. If the referee sees an infringement of the rules during your soccer game, he’ll penalize your team by awarding your opponents a free kick.