To arrest someone is to put them in custody for breaking the law. If you face arrest, your criminal activities will be "at rest" because you'll be behind bars, or in jail.
Arrest is both a noun and a verb. When you place a person "under arrest," you take them into custody and hold them so they can’t continue breaking the law. A police officer or other agent of the law will arrest a person often by physically taking them away. In addition to the legal meaning, arrest means "stop." To arrest motion is to stop a person or thing from moving.