In a manner similar to the way the devil tempted Christ in the desert as recounted in the Gospels of Matthew and Luke in the Bible, the White Witch tempts Edmund, who symbolically represents mankind, by appealing to his appetites, his love of power, and his ego.
The White Witch, realizing that she needs Edmund's cooperation to get to his siblings, first tries to tempt him into helping her by offering to satisfy his physical needs. Just as the devil tried to convince Christ to use his divine power to change stones into bread to satisfy his hunger, the White Witch first offers Edmund her mantle to shield him from the cold, then gives him something hot to drink to ease his thirst, and Turkish Delight to eliminate his hunger. Unbeknownst to Edmund, the Turkish Delight is enchanted. Anyone who has some "would want more and more...and would even...go on eating it till they killed themselves". Mankind wants to be comfortable, and is prone to the sin of gluttony, and the Witch, like the devil, uses this weakness to gain influence over her victim.
The White Witch next tempts Edmund with the offer of power. Just as the devil offered Christ dominion over all that He could see, the Witch says she will bring Edmund to her palace and raise him as her own. He would be a Prince, who "would wear a gold crown and eat Turkish Delight all day long", and eventually, "later on", he would become king, if only he would betray his brother and sisters to her. Mankind likes to feel that it has power and control, and again, the Witch tempts Edmund with the idea that if he does what she asks, he will be powerful, like a king.
Finally, the White Witch appeals to Edmund's ego, making him feel like he is pretty special, and that "it would be fun to keep...a secret between (them) two", without anyone else knowing. Similarly, in the Bible, the devil tempts Christ to use his divinity to test God. Mankind is disinclined to be humble, and the White Witch, knowing this, exploits this weakness in Edmund to gain influence over him (Chapter 4).