Humans have wanted to live forever for as long as we've lived at all. It's an obsession that stretches back so far that it feels like it's somehow hard-coded into our DNA. Over the years, immortality (to a greater or lesser extent) has been promised by everyone from religions and cults to the cosmetics industry, big tech companies and questionable food blogs.
It's also a staple of fiction, all the way back to the earliest surviving great work of literature. The Epic of Gilgamesh, carved onto stone tablets in 2100 BC, depicts its titular king hunting for the secret of eternal life, which he finds in a plant that lives at at the bottom of the sea. He collects the plant by roping stones to his feet, but then a snake steals it while he's having a pre-immortality bath. Gilgamesh has a little cry, then gives up.
The reason why we age is still the subject of major scientific debate, but it basically boils down to damage accumulating in our cells throughout our lives, which eventually kills us. By slowing that damage - first by making tools, then controlling fire, inventing writing, trade, agriculture, logic, the scientific method, the industrial revolution, democracy and so on, we've managed to massively increase human life expectancy.
There's a common misconception that to live forever we need to somehow pause the ageing process. We don't. We just need to increase the rate at which our lifespans are lengthening. Human lifespan has been lengthening at a constant rate of about two years per decade for the last 200 years. If we can speed that up past the rate at which we age then we hit what futurist Aubrey de Grey calls "longevity escape velocity" - the point we become immortal.