What is the Mass for?

I know I slept through most of my RCIA classes, but what is the Mass for if not to meet the spiritual needs of the people attending?

I’m sorry that you slept through your RCIA classes. Learning about God and the Catholic faith shouldn’t have to be boring!

The sacred liturgy is, above all things, the worship of God. Even if we were to get nothing out of Mass — we were distracted during the readings, or we didn’t understand them, the homily was replaced by a Bishop’s Annual Appeal video, and we did not receive Holy Communion (for whatever reason) — still, vere dignum et iustum est, aequum et salutáre, nos tibi semper et ubíque grátias ágere, Dómine, sancte Pater, omnípotens aetérne Deus, per Christum Dóminum nostrum.*

But there’s more to it than that, of course. Mass has four ends; the acronym “ACTS” or “PACT” has been used as a mnemonic.**

• Adoration
• Contrition
• Thanksgiving
• Supplication/Petition

Even when we don’t particularly feel contrite, the Mass calls us to contrition; even when we don’t feel like giving thanks, there is the Eucharist; even when we are struggling to adore God in the midst of natural disasters that take the lives of thousands and tens of thousands, the liturgy puts on our lips a Gloria or a Glory Be or an Alleluia; and even when we think we’re doing pretty well for ourselves, thankyouverymuch, the Prayer of the Faithful challenges us to be “poor in spirit” and to throw all our cares (and those of the whole world) upon the Lord. That’s meeting our spiritual needs, even when we don’t acknowledge we have them. (And the Mass is beneficial even for those who aren’t in attendance.)
All these ends are directed to the glorification of God: adoration and thanksgiving immediately so, and contrition and supplication mediately, for God is glorified in His mercy and generosity. Those latter two ends are directed toward our sanctification.

To be even more succinct, the Mass and the whole liturgy of the Church is directed to the glorification of God and the sanctification of humanity. That’s what Vatican II said several times:

Christ indeed always associates the Church with Himself in this great work wherein God is perfectly glorified and men are sanctified. (SC 7)

From the liturgy [...] the sanctification of men in Christ and the glorification of God [...] is achieved in the most efficacious possible way. (SC 10)

The purpose of the sacraments is to sanctify men, to build up the body of Christ, and, finally, to give worship to God. (SC 59)

There is hardly any proper use of material things which cannot thus be directed toward the sanctification of men and the praise of God. (SC 61)

The purpose of sacred music [is] the glory of God and the sanctification of the faithful. (SC 112)

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* "It is truly right and just, our duty and our salvation, to give you thanks always and everywhere, Lord, Holy Father, almighty and eternal God, through Christ our Lord."

** Another mnemonic, PART, uses "Reparation" in place of "Contrition".  Yet another is ALTAR: Adore, Love, Thank, Ask, Repent.