Checking when someone read your message is useful for all kinds of reasons, especially in a group chat setting.
To check, select the message and drag it left, revealing the time it was delivered and the time it was read. In a group chat, a list of who the message has been delivered to and who has read it shows instead.
Note: if you uncheck Read Receipts to prevent people from seeing when you have read their messages, you also won't be able to see when other people have read your messages (explained next).