I belong, to some degree, to the Catholic Charismatic Renewal. I attended the whole series of Life in the Spirit Seminars in my parish, and received the prayers known as “baptism in the Holy Spirit” by other members of the movement, including priests and deacons,
after the priest made a speech clarifying that this is in no way a sacrament or a “second baptism” but a prayer that aims at “stirring” the gifts of the Holy Spirit that we received in Baptism and Confirmation.
The formation was very solid. Fr. Raniero Cantalamessa wrote some very good books about it, and he has been for a while the Preacher of the Papal Household. So, one would say he’s a reputable source.
The praise & worship meetings are very nice. There are solidly Catholic songs and yes, there’s clapping and tambourines, but there’s also “gentle” songs, and even times of silence and contemplation. There are prayers, reflections, and activities to bring the “love in action” of the Holy Spirit to others.
Healing masses are not much different than a regular mass, except for the prayer of the priest over individuals who wish to be prayer upon, or the exposition and adoration of the Blessed Sacrament that may follow it.
Some individuals truly possess charismatic gifts of the Holy Spirit. I used to laugh at the idea, but as St. John says, once you see it with your own eyes, and you experience it, you know it is the truth. Some have gifts of healing, some do “speak in tongues”, some do speak prophetically, some “rest in the spirit”, and so forth.
Also the Charismatic movement is very active in the area of prayers of deliverance. Although professional medical counseling and a good sacramental life are the first steps for people who believe the devil is tormenting them, and exorcism is a rare practice, prayers of deliverance are a very legitimate ministry and sometimes the power of God reveals itself mightily.
The cultural element is important. Some places are louder than others. Other places are more quiet. Charismatic is a desire to let the Holy Spirit take control. It is not synonymous with “loud and happy-clappy”

In fact, there is an emphasis on contemplation and the practice of interior silence and frequent Adoration.
I was shocked when I started attending the Seminars and eventually became more involved. All my previous ideas were thrown out of the window. Except the “talking in tongues”. That is always a little odd. Like being in a foreign country. But while I used to think it was just mindless babbling, I heard some accounts that made me change my mind. For example, one of the members was “praying in tongues” and it sounded as usual, unintelligible, and another parishioner (not a member of the movement, just someone who happened to be at the chapel) asked the lady how she knew his native language and thanked her for her recommendations because they clarified a difficult situation he was praying for. As the Scripture says, “the finger of God is here”.