Why do Catholics pray to saints?
The short answer
Catholics ask the saints to pray for them for the same reason Christians ask friends to pray for them. Those who have died in Christ are alive with God, united to us in one Body, and Scripture shows them offering the prayers of believers before God's throne.
The communion of saints
The Apostles' Creed professes belief in "the communion of saints." The Church on earth, the souls being purified, and the saints in heaven form one family in Christ (CCC 954). Love binds them together, and so does prayer.
The saints are alive
Jesus says God "is not God of the dead, but of the living, for to him all are alive" (Luke 20:38). At the Transfiguration, Moses and Elijah converse with Christ about his coming death (Luke 9:30-31) — the dead are neither asleep nor unaware.
Scripture shows them interceding
In Revelation, the elders in heaven hold "gold bowls filled with incense, which are the prayers of the holy ones" (Revelation 5:8). An angel offers "the prayers of all the holy ones" before God (Revelation 8:3-4). Heaven is involved in earth's prayers.
Isn't Jesus the only mediator?
Yes — "There is also one mediator between God and the human race, Christ Jesus" (1 Timothy 2:5). But in the same passage Paul urges Christians to intercede "for everyone" (1 Timothy 2:1). Intercession within the Body of Christ shares in his single mediation; it does not compete with it.
A "cloud of witnesses"
"since we are surrounded by so great a cloud of witnesses" (Hebrews 12:1). The saints are both examples and friends. The Catechism puts it simply: "They do not cease to intercede with the Father for us" (CCC 956).