Relics are an invention of organized religion... and hollywood (i.e. "The Robe").
Relics are the bodies of the saints. Second-class relics are objects that the saints have touched. Nothing particularly "religious" about that.
Do relics have special powers? You be the judge.
Eucharistic Miracle of Lanciano
Blood of St. Januarius
Incorrupt bodies of the saints
Shroud of Turin
Sudarium of Oviedo
Scripture confirms the sometimes miraculous power of relics:
2 Kings 13:21Once while some Israelites were burying a man, suddenly they saw a band of raiders; so they threw the man's body into Elisha's tomb. When the body touched Elisha's bones, the man came to life and stood up on his feet.