Tests must provide fast, meaningful, and reliable feedback on quality and business risks. These are IMO the basic quality attributes of “good” tests.
Worth to mention are also the FIRST principles:
• Fast: Execute quickly
• Isolated: Have a single reason to fail
• Repeatable: Produce the same result when executed multiple times
• Self-verifying: Automatically detect whether they pass or fail
• Timely: Written concurrently with the code under test
Those principles contribute to the above mentioned attributes.