A wonderful bit of history...
Way back when Christianity had just started taking root, no one liked us. Jews thought we were fortune-telling zealots who should be smited for blaspheming against God in claiming that He became human and was crucified, the Romans thought we were political upstarts vying for civil war, and everyone else thought we were kooky cannibals who ate and drank each other's blood.
Ya know, or something to that effect.
As a result of this mass confusion regarding who Christians were and what we believed, folks tended to just relegate us to the fringes of society in the hopes that we'd eventually die off. When that didn't work, and our numbers began to grow, they figured they'd speed up the process by feeding us to the lions, torturing us to instill fear in potential converts, and very publicly putting us to death in a variety of cruel and creative ways.
As a result, Christians realized they needed to devise a more secure form of worship in which their lives wouldn't constantly be in peril.
We moved to the catacombs. We created communities in the middle of deserts, far from the authority of crazed sadists. We began using code language, and yes, we came up with the idea of sponsors.
The term "Sponsor" is synonymous with "Godparent." A sponsor is a person who is rooted firmly in Catholicism and agrees to help a newbie not only learn the ropes, but live those ropes through prayer, example and a life-long mentoring relationship. This is why the Church requires one sponsor to be a faithful, practicing Catholic for folks (children included) getting baptized / confirmed.
Anyway, the need for a sponsor back in the early Church ran a little deeper than just a mentoring relationship. Sponsors were the gatekeepers of Church activity. One could not become a vested member of the Church without a well-known sponsor stepping up and vetting you before acceptance by the community. This protected the Church from those who wished to infiltrate the now secret (and illegal) Christian communities that were blossoming throughout the empire.
The term "godparent" is synonymous with sponsor for good reason. Since there was so much martyring going on back then, children were many times left orphaned when both parents were arrested and taken to their execution for refusing to deny their faith. If the children were lucky enough to escape with their lives (and sometimes they were not), it was an unspoken agreement that the sponsor of the family would adopt the children and raise them as if they were their own (thus ensuring the salvation of their souls through the continued development of their Christian faith).
Nowadays, we continue the tradition set forth by our early members. Godparents are still supposed to be there as examples of true Christian living. Now these sponsors are typically chosen by parents for their children at baptism, but children have the option of choosing a new one at Confirmation.
However (and this is a big, important however), the Church strongly suggests that those preparing to be chrismated use the same sponsor they had for baptism. The reason for this is the strong connection between Baptism and Confirmation. Baptism, after all, is the 1st Sacrament of Initiation. This is the key that opens the flood of God's graces to us. We are cleansed of original sin and reborn in the Spirit. At Confirmation, our original baptism is perfected through the Gifts of the Holy Spirit. Our souls are once more marked with an eternal sign of the Spirit, and we are given untold graces that enable us to live out our Christian lives boldly and without shame.
This is actually the reason why the Church suggests that we receive Baptism and Confirmation BEFORE Holy Eucharist (the 3rd Sacrament of Initiation), but that's an entry for a different day.
So in a large nutshell, that is why we have Godparents.