Why do Catholics believe in saints?

The Bible teaches that Saints are those in Heaven with Christ:

"To open their eyes, that they may be converted from darkness to light, and from the power of Satan to God, that they may receive forgiveness of sins, and a lot among the saints, by the faith that is in me." (Acts of the Apostles 26:18)

Now, as for asking for the intercession of the Saints that comes from Tradition and Scripture.

From Scripture:

"And when he had opened the book, the four living creatures, and the four and twenty ancients fell down before the Lamb, having every one of them harps, and golden vials full of odours, which are the prayers of saints:" (Apocalypse 5:8)

"And another angel came, and stood before the altar, having a golden censer; and there was given to him much incense, that he should offer of the prayers of all saints upon the golden altar, which is before the throne of God. And the smoke of the incense of the prayers of the saints ascended up before God from the hand of the angel." (Apocalypse 8:3-4)

From Tradition (The Catechism of the Catholic Church):

"The intercession of the saints. "Being more closely united to Christ, those who dwell in heaven fix the whole Church more firmly in holiness. . . . They do not cease to intercede with the Father for us, as they proffer the merits which they acquired on earth through the one mediator between God and men, Christ Jesus . . . . So by their fraternal concern is our weakness greatly helped" (CCC 956)

"Communion with the saints. "It is not merely by the title of example that we cherish the memory of those in heaven; we seek, rather, that by this devotion to the exercise of fraternal charity the union of the whole Church in the Spirit may be strengthened. Exactly as Christian communion among our fellow pilgrims brings us closer to Christ, so our communion with the saints joins us to Christ, from whom as from its fountain and head issues all grace, and the life of the People of God itself": We worship Christ as God's Son; we love the martyrs as the Lord's disciples and imitators, and rightly so because of their matchless devotion towards their king and master. May we also be their companions and fellow disciples!" (CCC 957)