the trampoline analogy needs an extra source of gravity - because this is what the laymen, the recipients of the explanation, intuitively understand - but the real general relativity doesn't need any extra "external" gravity.

Instead, general relativity says that the space is getting curved by Einstein's equations,
$$G=T$$
where the left-hand side are numbers describing the curvature at a given point and the right hand side is the density of matter and momentum. I omit indices and constants haha. So general relativity says how the spacetime is curved under the influence of matter.

The second part of the story is that general relativity also says how matter moves in external geometry. It moves along "geodesics", lines that are as straight as you can get.
$$\delta S_{action\,ie\,proper\,length} = 0$$
This actually means that the objects move along the predicted, seemingly curved trajectories. These trajectories are actually as straight in the curved spacetime as you can get.

Imagine that there is a hemisphere  replacing a disk in the trampoline. So there exists a (nearly) straight line on the hemisphere - namely the equator near the junction with the rest of the trampoline. Note that the equator on the Earth is a maximum circle - so it is one of the straightest lines you can draw on the surface of Earth. The same is true for all actual trajectories that objects choose in spacetime of general relativity.

So in the hemisphere-above-trampoline example, particles can orbit around the equator of the attached hemisphere, just like planets, because it is the straightest and most natural line they can choose. I don't use any external gravity to explain the real gravity; instead, I use the principle that particles choose the most natural - the straightest - line they can find in the curved spacetime.

Best wishes
Lubos