We can clearly see Jesus giving this gift to St Peter:

And Jesus answered him, ‘Blessed are you, Simon son of Jonah! For flesh and blood has not revealed this to you, but my Father in heaven. And I tell you, you are Peter, and on this rock I will build my church, and the gates of Hades will not prevail against it. I will give you the keys of the kingdom of heaven, and whatever you bind on earth will be bound in heaven, and whatever you loose on earth will be loosed in heaven.’ (Matt 16: 17-19)

The Magisterium correctly interprets Scripture and Tradition, ie is able to give the correct way to understand Scripture passages or Catholic ways according to how God would want us to understand them. It usually does this by expressing teachings (also called doctrines or dogmas) about faith and morals.

“But the task of authentically interpreting the word of God, whether written or handed on, has been entrusted exclusively to the living teaching office of the Church Magisterium, whose authority is exercised in the name of Jesus Christ” (DV 10)

We believe that God keeps communicating with the Church. The Magisterium is expressed in two special ways.
Firstly, the pope can proclaim a teaching (this is called an ‘Ex Cathedra’ teaching on faith and morals which means ‘from the chair’ of St. Peter and happens very rarely). The last Ex Cathedra teaching was the declaration of the Assumption of the Virgin Mary by pope Pius XII in 1950. What the pope says on a daily basis is not part of the Magisterium, but it still maybe infallible.
Secondly, the Bishops, in union with the Pope, can gather together and declare teaching on faith and morals at a council. The creed is an example of when all the bishops proclaimed a teaching at an ecumenical council.

These two ways give Catholics (and the world) infallible teachings about God that express truths of the Word of God passed on through the centuries. The truth does not change, it is just expressed better.

To maintain God’s revelation through the centuries, you must have all three elements, Scripture, Tradition and the Magisterium. It is like a three legged stool. If one leg is missing it falls over.

“Sacred tradition, Sacred Scripture and the teaching authority of the Church (Magisterium), in accord with God's most wise design, are so linked and joined together that one cannot stand without the others.” (DV 10)