The unemployment-rate is a ratio whose denominator is the labour force, so it falls for two opposite reasons: people finding jobs, or people leaving the labour force entirely. Only the first is good news, and participation is how you tell them apart.
Participation also sets the ceiling on non-inflationary employment growth. When participation is rising, the economy can add jobs without wage pressure; when it is flat and demographics are shrinking the pool, the same job growth is inflationary.
Example: unemployment falls from 4.2% to 4.0% while participation falls from 62.7% to 62.4%. Roughly 500,000 people left the labour force, so the improvement in the headline rate is entirely an exit story.
Related: unemployment-rate, u6-unemployment, household-survey, nfp, nairu