Mass intentions are deeply rooted in Catholic theology.  There's also a temporal aspect to them, in that people offer a monetary donation* with the request for prayers by the priest at Mass for the living or deceased.
 
When the priest celebrates Mass, he offers each Sacrifice of the Mass for a particular person, or intention.  By doing so special graces from God are applied upon that person or intention.
 
Envelopes are at the back of the church.  Fill out and state who the Mass is intended to be said for and drop in any offering plate or give to Diane.  Your intention will be acknowledged with a Mass for those listed on your envelope.