The main issue of the story is that Dr. Alex Murray has mysteriously disappeared while working on a secret government project. The mysterious Mrs. Whatsit arrives at the Murray's home on "a dark and stormy night" and tells the Murray family there is a such thing as a tesseract (or, a Wrinkle in Time, as the book is named for).
Meg and Charles Wallace, children of Dr. Murray, along with the help of their friend Calvin, tesseract throughout the universe to try to find their father. Eventually, he's found on Camazotz, a planet ruled by a dark force referred to as IT. Dr. Murray manages to tesseract out of the planet with Meg and Calvin, but Charles Wallace is left behind under the thrall of IT. Meg uses the power of her love for her brother to save him, and they all tesseract back to Earth.