The universe is vast, being around 93 billion light-years across, but we will only ever be able to reach 6% of it. Here is why.
The End of Star Formation:
As you may already know, stars will eventually burn out, but what keeps the cycle going is the formation of new stars. As time continues to go on, the formation of stars gets slower and slower and will eventually come to a stop. 95% of the stars that will ever live have already been born, and only three new stars are born per year in the Milky Way galaxy. Eventually, all the stars in the universe will burn out, and there will be darkness.
Galaxies, Superclusters, and Cosmic Neighborhoods:
The Milky Way is a galaxy that is part of the "local group" of about 55 other galaxies and 10 million light-years across. Hundreds of local groups make up the Laniakea Supercluster, and many superclusters make up our cosmic neighborhood. In total, there are around 2 trillion galaxies in the observable universe, but we will only be able to access 6% of them. This is because the universe is expanding faster than we can reach the galaxies. Even traveling at light speed wouldn't be enough to reach galaxies, local groups, or even other cosmic neighborhoods, meaning that we are bound to our cosmic community and cannot travel out of it. Such a large percentage of the universe's inaccessibility has to do with the expansion of the universe, starting with the Big Bang.
The Expansion of the Universe:
At the beginning of the Big Bang, the singularity that held all the energy and mass of the current universe started to expand suddenly. In an extremely short time, it had grown into a small bubble of energy. This bubble was not uniform, and some parts were less dense than others. As this bubble grew larger and larger, these less dense areas grew in proportion to the size of the bubble, forming pockets with a stronger gravitational pull or cosmic neighborhoods. This means that our cosmic neighborhood, or gravitational pocket, is surrounded by other cosmic neighborhoods that aren't connected. Because of a force we don't yet understand, dark energy, the spaces from one cosmic neighborhood to another are expanding, increasing the distance needed to travel from one neighborhood to another exponentially. The speed of this expansion has reached faster than the speed of light, making it unreachable forever.
How Galaxies are Still Visible:
The information that reaches your telescope is in the form of light. The light from galaxies far away is made of photons that travel at the speed of light, and even light takes time to reach Earth, hence the name light-years. For example, the light from a galaxy three million light-years away will take three million years to get Earth, and once it does, the observers will be seeing the galaxy as it was three million years ago. This also applies to galaxies that are inaccessible (their photons are still traveling to Earth).
Most of the universe will be inaccessible to us, but that doesn't stop scientists from exploring the universe with the information we have. We barely scratched the surface of our solar system, let alone our cosmic neighborhood!