Circumflex accent (caret)

Usually “this” or “I agree with the message above.” The caret looks like an arrow pointing up, so a reply of just ^ backs whatever was said right before it. More carets (^^^) push harder. It is not a correction and not sarcasm by default. In a fast group chat, though, it points at whatever sits directly above, which may not be the message the sender meant.

Doubled up, it turns into a face. ^^ or ^_^ are two happy, squinting eyes, a style of emoticon from Japan and Korea read the right way up. ^^; adds a drop of sweat: an awkward or embarrassed smile.

Why is a hat on the keyboard at all?

It started as an accent that typewriters put on letters. A typist could strike ^, back up and type e over it to get ê, as French and Portuguese need. Many European keyboards still treat it that way: the key does nothing until you type the next letter.

Computers then gave the free-standing mark new jobs. Without a way to raise small numbers, people wrote powers as 2^3, and calculators and spreadsheets read it the same way. Programmers use it too, for example to mean “start of the line” in search patterns. Its English name, caret, is borrowed from the proofreader's mark ‸ for “insert something here”.