Traditionally, peruse has meant to read or examine something carefully. But informally, it can have the opposite meaning, to read something casually and quickly.
To understand the two meanings, think about the way people like to talk about doing things thoroughly, even when they aren't. If you are visiting a library or a bookstore, you might find yourself perusing the shelves. Synonyms are browse and skim. Peruse is from Middle English perusen "to use up," from the Latin prefix per- "thoroughly" plus Middle English usen "to use."