I've checked 3 times already in reading this thread to make sure I was in the spirituality forum

I think perhaps it would be better placed in psychotherapy or self help?

But, with regards to the spiritual aspect of this phenomena, I will respond, OK?

For catharsis to occur one needs a type of abreaction. I would give example of realizing you are lost in your sin and when you die, you are not going to heaven. Then, you hear of God's love and His salvation paid for by Christ, and you, perhaps sobbing from your guilt and fear accept this Payment for your sin. The carthartic prayer occurs, along with the resulting freedom of the doom and gloom.

(Not everyone who accepts Christ has such a sequence (abreaction-cartharsis) and it isn't required for salvation.)