The main problem with this analogy is that the thing it's trying to explain (gravity) is tangled into the analogy (balls bend the sheet because of gravity) so i

The main problem with this analogy is that the thing it's trying to explain (gravity) is tangled into the analogy (balls bend the sheet because of gravity) so it doesn't provide an independent viewpoint. On first encounter this analogy seems to lead to great enlightenment but a bit of thought reveals that it doesn't really explain anything, even in simplified terms. It's not hard to summarize the basic tenants of GR, here is a very good attempt: http://physics.stackexchange.com/a/3018/852 http://physics.stackexchange.com/a/3018/852. For a layperson I would focus on (1), what a geodesic means (what's the shortest way to travel from NYC to London, etc.). Then I would move to (2) and say that we don't know why that is the case. This would be a nice segue into a discussion about how Physics just describes observed phenomena with equations and the explanations are iterative.