> It's based on people who for the following three criteria. They: 1) don't have a job, 2) have looked for a job within the previous four weeks, and 3) are available to work at the present time.

You're correct.

To add to that, in some cases (such as layoffs), even the second criteria can be relaxed. For example, if a person is laid off but expected to be recalled, they don't need to have job-seeking activity to be considered unemployed for statistical purposes. That's just one example.