Keep in mind that "infringement" means to limit or undermine something. Most commonly, infringement is used in the context of intellectual property or contracts. A typical infringement case involves intellectual property, which means that someone uses something like an image, a logo, or a slogan, belonging to someone else, without lawful permission. In such a case, the owner of the intellectual property, the plaintiff, can sue for damages. Damages in this case could be something like lost profits of the plaintiff or the profits gained by the defendant. In short, damages would be defined by the court or by a jury in a monetary amount. In addition to damages, the plaintiff can sue for an injunction. An "injunction" is an order from the court requiring the defendant to stop the infringement. It is enforceable by the contempt powers of the court, which means that if the defendant does not stop, he or she can be sent to jail.
In addition to intellectual property infringement, there is such a thing as infringement on constitutional rights, contract rights, and any other rights recognized by the law. Generally speaking, this kind of infringement means that an individual is interfering upon another person's rights, granted by the constitution or a contract, or some other legally recognized agreement. In such cases, the same is true as for the above. The plaintiff can sue for damages and/or an injunction.