"What was visible in Christ has passed over into the Sacraments"
- Pope Leo the Great
The Sacraments are special ways in which we encounter Christ and His saving work. The traditional definition is that they are efficacious signs, instituted by Christ, to give grace.
The sacraments are sacred signs- symbols in a deep sense. They are comprised of sensible words, actions, and materials, which point beyond themselves to the invisible activity of God. But they don't only point to the action of God- they are efficacious signs- meaning that what they point to, God actually does, through them.
So in baptism, for example, the water signifies washing, dying, and being reborn. But these are what actually happen spiritually when someone is baptized. So the water symbolizes being cleansed from sin, but through the water and the words, God actually cleanses the person of sin! The sacraments are amazing!
Catholics believe that the 7 sacraments were, in some way, given to us by Christ. While their exact structure has evolved through time, the core reality behind them goes back to Jesus.
This is how we distinguish between things which are essential in the Church, and which, while good, are simply additions to the core faith. Since the sacraments are instituted by Christ, it means that we cannot get rid of them, and we cannot change them in their essence. This is why we take the sacraments so seriously, and do not make changes to the way they are celebrated. Jesus gave them to us so that His salvation could be made effective in us- they are the core of what we do as the Church!
The purpose of the sacraments is so that we can encounter God and receive His grace. "Sacraments are 'powers that come forth' from the Body of Christ, which is ever-living and life-giving. They are actions of the Holy Spirit at work in his Body, the Church. They are 'the masterworks of God' in the new and everlasting covenant" (Catechism of the Catholic Church, paragraph 1116).
"Grace is a participation in the life of God" (Catechism, 1997). Jesus came to fill us with His very life, and the sacraments are the preeminent way in which He does this.