Religious undertones exist both in Harry Potter and the Sorcerer's Stone and in the series as a whole. As mentioned in the other answers, Harry is a Christ figure, a chosen one who is destined to end the tyranny of Voldemort, who represents evil.
Sacrificial love is a strong concept in the Christian religion, since Christ's love for humanity led to the cross, and it is much the same in Harry Potter and the Sorcerer's Stone, where Harry's mother died saving him. Her love continues to protect Harry from evil, as represented in Voldemort when Quirrell tries to kill Harry during the climax before the Mirror of Erised. Harry is knocked unconscious during this confrontation, which is presented as a metaphorical death, since he confronted Quirrell in order to protect the school and, indeed, the wizarding world at large from Voldemort.
The Sorcerer's Stone itself contains religious connotations as well. The stone is said to grant eternal life, which is why Voldemort wishes to possess it. In contrast, Harry is willing to risk his life to procure the stone but not use it. This element of the story could be linked to the Bible verse Matthew 16:25, "For whosoever will save his life shall lose it: and whosoever will lose his life for my sake shall find it." At the end of the novel—and at the end of the series—Voldemort's violent quest for immortality ends in death, while Harry, who sacrifices time and again, ultimately gets to live a life filled with love and companionship.
The unicorn blood has similar religious significance. In medieval Christianity, the unicorn was a symbol of Christ, since it was associated with purity and goodness. To kill a unicorn is to kill something truly good. As Firenze tells Harry in the woods, "The blood of a unicorn will keep you alive, even if you are an inch from death, but at a terrible price. You have slain something pure and defenseless to save yourself, and you will have but a half-life, a cursed life, from the moment the blood touches your lips." Firenze's lines are reminiscent of the biblical verse "What will it profit a man if he gains the whole world, yet forfeits his soul?" (Matthew 16:26). Voldemort's killing a unicorn further cements his position as an evil, even Satanic, figure, opposed to the values represented by Harry, the Christ figure protagonist.