It’s important because the Fed is interested in the NAIRU - non-accelerating-inflation rate of employment.

Below a certain level of unemployment, the NAIRU models expect wage inflation (companies offering higher and higher wages to get new employees in a tight labor market) which drives inflation in the broader economy. This model kind of assumes that the labor force is inelastic. In reality if unemployment were low, a lot of “unemployable” or underemployed people would probably start looking for jobs, which makes it so current unemployment rates don’t accurately reflect how close we are to NAIRU.