There are multiple conflicts in A Wrinkle in Time. The major conflict is the struggle between good and evil.
The first problem presented in the story is the fact that Meg's father is missing. This leads to conflicts at school, as there are rumors that Meg's dad left his family. Other conflicts at school include Meg fighting with another student who insults her brother, and Meg's teachers suggesting that she be held back a year. This also adds to Meg's internal conflict of not believing in herself.
Meg learns that her father is fighting the Dark Thing, and along with Charles Wallace and Calvin, she must join the fight in order to save him. The Dark Thing has been moving in on Earth for a long time, and people like Buddha and Bach have been fighting it.
On Camazotz, the man with the red eyes gains control of Charles Wallace. They find Meg's father and are able to break him out of the cell, but now they must face IT. Meg is almost taken by IT, until Mr. Murray "tessers" them out of there. This causes conflict between Meg and her father, as she is angry her father left Charles Wallace behind.
Meg is the only one who can save Charles Wallace. This is the major conflict of her using love to face off against the forces of evil. It also causes Meg to face her internal conflict, as she must believe in herself and embrace the love in her life.