The sun will run out of hydrogen to burn in about 5 billion years, and then it will start fusing heavier elements, until it eventually runs out and collapses.
As the Sun comes to the end of its life, when the reactions that fuse Hydrogen atoms to form Helium stop, it will start to cool and expand into what we call a ‘Red Giant’ star, burning the Helium instead. It will grow so large that Mercury and Venus really won’t stand a chance, and will be ‘eaten up’! Earth probably won’t do too well either, since it will then be very close to the Sun.. but don’t worry – we have billions of years until this happens!
Next it will collapse in on itself to become a ‘White Dwarf’. The Sun isn’t heavy enough, but other stars will ‘explode’ as a Supernova at this point instead, becoming incredibly bright and blowing off gas and dust in a fiery, dramatic death.
The Sun isn’t big enough to blow up, so as Jane and Helen said, it will sort of give up eventually and settle down t o a hot ember, about the same size as the Earth, not that there will be much left of the Earth by then!
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