Pentecost commemorates the descent of the Holy Spirit on the disciples after Jesus’ death. You can read about it in Acts ch. 2, or meditate on it during the third Glorious Mystery if you pray the rosary.
Remember, immediately after the crucifixion, they were hiding in locked rooms in fear. Jesus appeared to them over a period of 40 days (Acts ch. 1) before ascending into heaven. At Pentecost, however, the Holy Spirit descended upon them, filled the entire house in which they were staying, and they began to speak in tongues so that everyone who heard them heard them in his own native language. Peter goes on to connect the day’s events with the prophecy of Joel 2:28-32, and began to boldly preach, and won thousands of hearts.
So Pentecost represents the turning point of the Church, where it becomes fortified by the Holy Spirit and boldly proclaims itself to the world instead of hiding in fear for its lives.
Liturgically speaking, Pentecost happens about 7 weeks/50 days after Easter (hence the ‘Pente’) and ten days after Ascension Thursday. It marks the end of the Easter season, and in the Latin rite, the priest changes his vestments from the white of Easter to the red of the fire of the Holy Spirit. The next week marks the beginning of the green of Ordinary Time. (Today’s 3rd Sunday of Ordinary Time used to be referred to as the third Sunday after Pentecost, for example.)
Historically speaking, Pentecost was often referred to as Whitsun, and used to be popular for baptisms and commemorating the gifts of the Holy Spirit.
Since it always falls on a Sunday, we always commemorate it.
Whether or not we notice what we’re doing is up to the individual.
