What does “don't trust verify” mean on Bitcoin Twitter?

Could you explain the phrase "don't trust, verify" as it's commonly used on Bitcoin Twitter? I've seen it pop up quite often but I'm not sure exactly what it means or why it's important. I understand it has something to do with verifying information and not blindly trusting everything you read, but could you elaborate on that a bit more? I'd appreciate a detailed explanation of the concept and its relevance in the Bitcoin community.