A chat message that gets starred has a star next to it:
It means that someone found your message useful or funny or interesting... or just wanted to give you a star for some reason. They can be pretty arbitrary sometimes.
There's more information in the Chat FAQ:
You can star both rooms and messages by clicking the star next to the respective item.
Feel free to star any message you feel is particularly useful or worthy of summarizing in the transcript. You can star a maximum of 20 messages per room per day. Messages can be starred by anyone in the room; the more stars, the more interesting the message to that room.
Starred messages appear in the room sidebar, ordered by number of stars and last time of starring. (Room owners can also pin messages, which permanently affixes them to the top of the room sidebar for up to 14 days.) The room sidebar is intended to be a collaboratively created mini-timeline of interesting room events for people who don't have time to read the entire chat transcript for that particular room.