Eventually, though, mutation would have led to the birth of what could be considered the first modern human. It would have bred with the other local homonids and because it was more intelligent, its children (who shared those genes) would live longer than the children of the less intelligent homonids. After several generations, only the modern humans would be left alive.
Exactly when "modern people" arose and what separates us from the animals remains a point of contention among biological anthropologists (scientists who study humans). Would the first human have been lonely surrounded by his or her less intelligent relatives? Did human intelligence develop gradually? Were there creatures half way between us and them? Did the first human have a soul?
As there are no living missing evolutionary links, these questions remain unanswered, but that doesn't mean that people won't keep searching for answers.
If you believe in God, perhaps He intervened in evolution and gave humans the thing that separates them from the animals; perhaps aliens left us here on a mission to colonize the universe; or maybe our free will is an illusion and we're no different from any other animal.
Philosophers, scientists, and theologians have spent their lives trying to divine the origin of humanity, so don't beat yourself up if it's not crystal clear.