Yes the Earth will die some day. Even if we stop polluting the Earth, it will still die. The Sun uses hydrogen to to generate heat and light, but eventually it will run out of hydrogen. When it does this it will expand and cool down. It will become what is known as a red giant.
Red giants are huge.
And the heat from the Sun will make our seas boil and our atmosphere disappear. But as I said, this won't happen for another 5 billion years or so. The other way the Earth could die is if we continue to pollute it. By generating lots of greenhouse gases we'll eventually heat the Earth up so much that life on Earth might not survive. The acid rain we produce and the chemicals that destroy the ozone also cause problems.