Roman Catholics celebrate the Feast of the Chair of St. Peter every 22 February. The celebration marks a day in the year for a more unified prayer for the unity of all Christians at the head of the Seat of Peter.
The Seat of Peter (Office of Peter, Cathedra of Petros, Chair of Peter) is the first episcopal (bishopric) office created by God the Son, Jesus Christ during his earthly life sometime about 33AD. This Chair is similar to the modern-day rendition of a presiding officer such as the chairman (or chairperson) or head. Since Peter (based on tradition) last lived and died in Rome, it is correct to reason out that the Seat of Primacy among the bishops resides in the Roman Pontiff (bishop).
This Seat or Office has many functions just like that of the Seat of Moses.  Anyone who sits on that Seat is in a sense infallible. Infallibility (cannot be wrong in what is said) on the other hand is totally independent of impeccability (not being able to sin). The doctrine of infallibility is that the any current Pope (the one who sits at the Chair of Peter) cannot err on their promulgation / definition of doctrine in matters of faith and morals — that is, declaration of those truths/proposals that are helpful for the salvation of souls. 
While many would paint this Seat full of earthly powers, one may consider it so because as recorded [Mt 16:17-19] in Jesus’ words:
“Blessed are you, Simon son of Jonah, for this was not revealed to you by flesh and blood, but by my Father in heaven. And I tell you that you are Peter,b and on this rock I will build my church, and the gates of Hadesc will not overcome it. I will give you the keys of the kingdom of heaven; whatever you bind on earth will bed bound in heaven, and whatever you loose on earth will bee loosed in heaven.”
One could look into the loosing and binding sequences: both starts from earth! When the “keys” looses (or binds) on earth through the ministry of the Pope, heaven follows! This is not just earth-shattering powers but heaven shattering as well!
As there could only be one person seating in that Office, many would fear of possible tyranny and evil that may arise. But with the promise of the Catholic Founder Himself,
“Simon, Simon, Satan has asked to sift all of you as wheat. But I have prayed for you, Simon, that your faith may not fail. And when you have turned back, strengthen your brothers.” [Lk 22:31-32]
I am with you always, even to the end of the age. [Mt 28:20]
The same also promised of the aid of the Holy Spirit:
But the Helper, the Holy Spirit, whom the Father will send in My name, He will teach you all things, and bring to your remembrance all that I said to you. [Jn 14:26]
If at any chance that the Church has failed, then we can truly say that God has failed in all these checks and balance. But since He is God, the plan cannot fail. Therefore, the true Church stands erect even to this day. Just as Peter initially denied Jesus three times, he eventually repents and became the true leader and pillar of the Church. In the same sense that his Office (The Chair of Peter) will stand in all the trials and cannot be destroyed even by the one who sits on it — even Death and the Gates of Sheol/Hell.
In the words of the wise Gamaliel :
“… if it is from God, you will not be able to stop them. You may even find yourselves fighting against God.”
 The salvation of souls is not the process of preventing from something bad to happen. Salvation is something like leading something towards its more perfect state. For human souls, it is attainment of their ultimate goal: to live with God. Humans are meant to live perfectly with God in their human form — body and soul — consistent with the dogma on the Resurrection of the Body.
 Quoted from Acts 5:39. Gamaliel is one of the Pharisees who are revered by many during the persecution of the Apostles. See wikipedia entry.