Police can't arrest you without probable cause — a fact-based reasonable belief that you've committed a crime. An arrest without it is a false arrest and a Fourth Amendment violation. The standard is lower than "beyond reasonable doubt" but higher than a hunch — it's what a reasonable officer, looking at the same facts, would conclude.
Below the arrest line is the Terry stop — a brief investigative detention, named after Terry v. Ohio (1968), that requires only reasonable suspicion of criminal activity. Police can stop and ask questions, and pat you down for weapons if they reasonably believe you're armed and dangerous. They can't stop you just because you "look suspicious," because of your race, or because you refused to answer questions on the street.