How did Meg's father disappear?

This is one of the key questions in A Wrinkle in Time. Early in the story, no one has any idea what happened to Meg's father. In chapter three, Calvin and Meg are having a conversation, and Calvin asks Meg about her dad. She responds,

He's a physicist.

This is a fact commonly known around the town. The community also knows about a rumor that he ran away with another woman and left his family. Meg, however, does not agree with this story and tries to run from their conversation when Calvin brings up this rumor. Meg decides to continue talking, and she shares that her father worked for the government and that his work was top secret. Few people know what project he was working on. Meg tells Calvin that one day the letters her father regularly sent to her family stopped coming.
Calvin questions whether he might have died, but Meg boldly denies this. Instead, she holds onto hope that he is okay, trusting what the government told her mother:

She's been down to Washington and everything. And all they'll say is that he's on a secret and dangerous mission, and she can be very proud of him, but he won't be able to—to communicate with us for a while. And they'll give us news as soon as they have it (chapter 3).

Early in the story, no one, including Meg and her mother, is aware of what has happened to Meg's father. Later, readers find out that he was taken by It, an evil villain, to the faraway planet of Camazotz. He still deeply cares for his family. Ultimately, Meg ends up more involved in her father's secret government mission than she ever dreamed possible.