A tesseract is the fifth dimension which allows people to travel through space quickly by folding space together. If that doesn't make sense to you, you're in good company. It didn't make sense to me or the main character, Meg, either. Here's how Mrs. Who and Mrs. Whatsit explain it:
Mrs. Who took a portion of her white robe in her hands and held it tight. "You see," Mrs. Whatsit said, "if a very small insect were to move from the section of skirt in Mrs. Who's right hand to that in her left, it would be quite a long walk for him if he had to walk straight across."
Swiftly Mrs. Who brought her hands, still holding the skirt, together. "Now, you see," Mrs. Whatsit said, "he would be there, without that long trip. That is how we travel.
And ever since reading that, I've wished I could travel by tesseract.
— Carly H., STACKS Staffer