The popular view of Mormonism is that when you die, you get your own planet. Here is a more precise statement of the view from the Wikipedia article on Mormon Cosmology:
Mormon cosmology teaches that the Earth is not unique, but just one of many inhabited planets, each planet created for the purpose of bringing about the immortality and "eternal life" (i.e., the highest degree of salvation) of humanity.
There are millions of Mormons and billions of Christians. At the time Mormonism was founded, it was not clear how many planets there were outside the solar system-- many planets were undiscovered. It might have been a stretch in the early years of Mormonism to claim there were enough planets for every possible believer.
Even if we limit our view to Nicene Christianity, it is clear that there was a command to multiply:
God blessed them and said to them, "Be fruitful and increase in number; fill the earth and subdue it. Rule over the fish in the sea and the birds in the sky and over every living creature that moves on the ground." Gen 1:28
Many have held that physical death (i.e., a limited lifetime) was not in the original plan for God's creation. A command to multiply and no death logically leads to geometric progression of population. If there's only one planet, it probably would fill up soon.
But the universe is immense. My favorite measure of the immenseness of the universe is that one previously-thought dark region of sky, when examined by The Hubble Telescope, was shown to contain 10,000 galaxies.
Thus, a plausible reason for the immense universe is to provide homes for an unfallen, geometrically increasing population of humans. It provides an apologetic argument for God's providence that would not be there if say, the observable universe had consisted of merely the island of Bermuda.
While it's clearly implausible for humans, in their current fallen state, to travel to far galaxies without any Divine intervention, "all things are possible with God."