And yes, life on this Earth will someday come to an end. In the far future of the Solar System, the Sun will get too hot for the Earth to possess liquid water on its surface; the oceans will boil away. After that, the Sun itself will expand into a red giant, blow off its outer layers and contract down into a white dwarf: a stellar corpse. While there are many, many subsequent generations of stars that are yet to form — a process that will continue for many thousands of times the present age of the Universe — at some point, the available fuel for new stars will be gone.
Beyond those timescales, the stars will one-by-one be ejected from all the remaining galaxies, left to wander the infinite abyss between the cosmic island Universes. Except for the quantum motion inherent to atoms themselves, everything will cool to an arbitrarily close-to-absolute-zero temperature. And on even longer timescales, black holes themselves will evaporate, giving rise to a frozen, empty cosmos.
This is known as the “heat death” of the Universe. While there are other speculative possibilities, such as the Big Rip (where dark energy increases over time), the Big Crunch (where something causes the Universe to recollapse), a cyclic model (where a series of bangs-and-crunches occur), or a new phase transition that enables new material to be created, the heat death (also known as the Big Freeze) appears to be what the data of the Universe favors at the present time.