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Nails are a protective layer that hardens from the same material as hair (keratin), but denser. They're there to protect your fingertips from injuries and infections, plus they help you pick things up, scratch an itch, or deal with small objects. They grow your whole life because the tips constantly wear down and break - your body just replaces the loss, like it does with hair. If you don't trim them, they'll break on their own, but this way you're in control of it.
The usefulness of nails becomes obvious when you imagine fingers without them - it immediately becomes clear that fingertips are much more vulnerable to scrapes, splinters, and infections. But that's not their only function. Nails work as a tool: you can use them to pry something open, scratch, clean stuff, comb your hair. Try opening a jar or peeling an orange without them - it's pretty inconvenient. Plus they slightly enhance the sensitivity of your fingertips, improving your sense of touch.
As for growth - that's just basic biology at work. Nails grow from special tissue at the base called the matrix, which constantly produces new keratin cells. Over time, the outer layer wears down, flakes off, and gets damaged, so your body simply compensates for those losses with new growth. It's similar to hair or the top layer of your skin - everything's constantly renewing and shedding. Growth slows down with age and depends on your health, nutrition, and genetics, but it basically never stops as long as you're alive.
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