Finding life on another planet, even just single celled organisms, would help with the study of biogenesis, which is one of the greatest mysteries of biology.

Some exotic life form, which did not originate on earth would most likely have interesting features we have never seen before. Scientists could study them and gain insights about alternatives to the biology of earth creatures. Who knows this research may lead to new drugs or procedures we can use to better our lives?

Depends if it's life that has common ancestors with us or not.

If life originated independently twice in our Solar System it means whole galaxy should be teeming with it.

It doesn't look like it does - so the Great Filter moves from "rise of life" to "rise of complex life", "intelligence", and "technical civilization".

That's very bad news for u,, it dramatically increases the odds that technical civilizations usually destroy themselves soon after they develop.

Among others mentioned in this thread is: who knows? It's an unknown unknown

Maybe nothing. Maybe nanotechnology. Maybe information storage. Maybe photosynthesis. Maybe physics, math. It would almost certainly radically transform biology. One thing is certain: it wouldn't likely have zero effect on human understanding

It would have significant implications for our long term future (or lack thereof).

I'd probably think about it occasionally and smile.

It would change our science fiction.

Children would learn about it in school from a very young age, or at home in books even younger. They'd grow up knowing Earth life isn't the only life.

Religions would slowly adapt to be more palatable to children who grew up this way, or lose favor among the next generation.

Finding proof of the existence of God would not change anyone's lives materially, but you know why it would be important.