Imagine you have a picture of your favorite toy. Image-based modeling and rendering is when you use that picture to make a 3D model of that toy and then create a new image that looks like it's actually there in real life.
First, you take the picture and use special computer software to figure out where everything is in the picture. That means you tell the computer where the top and bottom of the toy are, where it's thick and where it's thin, and all of the details in between.
Once the computer knows what the toy looks like from one angle, it can use math to figure out what it would look like from all different angles. That's how it can create the 3D model of the toy.
Then, the computer can create a new picture of the toy in a different environment. Maybe it's in a room or in a park. The computer can make the toy look like it's actually there by adding shadows, reflections, and other things that make it look like it's part of the real world.
Overall, image-based modeling and rendering is like taking a picture and turning it into a 3D model that looks like it's in real life.