I'm so glad you are helping your child as they learn to write. Teachers have different ways of helping children develop a topic. Drawing a web and drawing a diagram are two different ways. These are also sometimes called "storyboards." Basically, the idea is that you want to brainstorm some ideas before they sit down to write so that you don't just sit and look at the page. You may have learned to outline or jot down notes, which are similar ways to do this. I'd always suggest that you read the teacher's instructions and ask your child what they remember about the directions first. However, if you still aren't sure, here is how I would interpret that instruction:
1. Write the topic idea in the middle of a piece of paper. I usually tell my students to frame this as a question. By the way, expository is usually an argument essay and one kind of argument essay is a problem solution. For example: How can we solve the problem of students being absent too often from school?
2. Draw a circle around that question and then draw lines out from the circle (looking like you are starting a spider web). Each of the lines should be an answer to the question. Example: make them go into detention, call the parents, give them incentives for having good attendance, give them a chance to not take the finals if they have good attendance, etc.
3. Then draw a circle around each of those answers and draw lines off again. This time, you will give examples, reasons or objections that relate to that answer.
By doing this, your child will have some information that they can use to write their paper.