Things that enrage you make you mad. Really mad. People are not typically enraged by annoying things like paper cuts or long lines. They are more likely to become enraged by evil or injustice.
Something that enrages you makes you incredibly angry. The news that their favorite teacher has been fired might enrage a group of students, and witnessing someone mistreating an animal might also enrage them. The 14th century verb enrage combines the prefix en-, "make or put in," and rage, with its Latin root rabies, "madness, rage, or fury."