An observer is someone who watches or pays attention to something — if you're an observer of current events, you probably watch the news and read the newspaper every day to keep up with what's going on.
You can be an accidental observer of something, like pedestrians who happen to witness an accident and become observers of it. Another kind of observer is one who notices things deliberately, like political observers who watch and comment on various events. Many newspapers once had the word observer in their names, from this second sense of the word. The verb observe has a Latin root, observare, which means "watch over, note, heed, or attend to."