I'll add to what Ariel said and first suggest that you post in your classroom this quotation by Isaac Asimov: "Education isn’t something you can finish."
Secondly, I would compliment the student on asking such an excellent question. It is exactly these "why" kinds of questions that scientists work on answering. That's basically what science is -- finding explanations for phenomena that we observe. (And there's no five-step procedure for doing this, i.e., no single "scientific method.")
As has been suggested, for most questions that I don't know the answer to, I'd work with the student to find answers. But, as you've discovered, that's more difficult for this question.
A complete explanation of gravity isn't practical for a 3rd-grader. (I explain why that is below.) However, you can do the following to provide a bit of insight into one of the relevant ideas:
Take an Earth globe and point to two, widely separated places on the equator. Say to the student: Imagine that there are two people who start at those points and both agree to walk (or swim, as needed) due north. They're initially not moving toward each other, but along parallel paths. After a long time of traveling, they will eventually meet at the North Pole. How is it that they ended up together when they started out walking along parallel paths, separated from each other? (On a flat, Mercator-projection map of the Earth, the two paths really do appear parallel -- along two lines of longitude.) If the travelers didn't know that the Earth is round (i.e., spherical), they might think that there was some force that pulled them together. Someone like Isaac Newton might give this force a name, like "gravity." But someone else, like Albert Einstein, might come along and explain, "No, there was no force pulling you together; rather, you were simply moving on a curved surface. And that curvature caused you to come together without any extra forces being needed."
You can imagine a similar situation with objects (like an apple) falling toward the earth -- not because there's a force (gravity), but because they are traveling through curved space.
FYI, Chelsea, that was a highly simplified analogy and, like many analogies, not correct in all respects. For example, it's actually both space and time that are curved. So, Einstein's General Theory of Relativity deals with the curvature of "space-time" as a single entity.
I would also tell the student: "To really understand this (which would be a great thing to do!), you'd have to first learn a whole lot of physics -- which you can do in high school and college."
The reason I said above that a complete explanation isn't practical for a 3rd-grader is that, before understanding how gravity works, one first needs to understand about Newton's laws of motion, Newton's law of gravity, inertial reference frames, Einstein's Special Theory of Relativity, and the Equivalence Principle. Only then can one think about how gravity is explained by a four-dimensional curved space-time, and how free-falling bodies move on "geodesics" in spacetime.
If the student is really interested in stuff like this (and who wouldn't be? :), she or he should consider becoming a physicist or an astrophysicist.
I hope that helps.