Here's the best explanation to your query:
First, I would like to point out that I am talking only about expansion due to the initial inflationary event. i.e I am ignoring any effects of dark energy on the expansion.
As we know the universe is expanding. What this means is that the distance between any two points in space is increasing. Now, this expansion is NOT the result of a force, but is rather a product of inertia. Simply put, the initial expansion event (likely inflation) that occurred in the early epochs of the universe started the expansion. Objects, following Newton's first law, simply continued to expand and go about their business in the absence of any external force.
If you must think of the big bang as an explosion of sorts, all the pieces are simply flying away from each other, governed by inertia, NOT some force compelling them to fly away.
So, now that we have established that expansion is merely the natural tendency for bodies to move under their own inertia, it becomes obvious why gravitationally bound systems are not expanding. Once gravity comes together strong enough to effectively nullify the initial "push" of the inflationary event, the system is no longer in an expanding state. Once the expansion has been stopped, since there is no "expansionary force", there is nothing to cause it to expand so the system evolves under its own gravity.
This is why dense clumps of matter (galaxies, solar systems, and the like) do not expand.
Now, my initial assumption was no dark energy, because I believe that is the model being discussed here anyways. With the inclusion of dark energy, there is some force causing an expansion, so you can modify the above logic accordingly.
I hope this all makes sense, this was my best attempt at wording a sometimes unwordy concept.
Cheers!
