This is perhaps best explained in a video:
The gist is that hydrogen is fused into helium and the gravitational force balances out the nuclear forces. Eventually, hydrogen will run out and the sun will collapse because of gravity. But that will eventually create conditions sufficient enough to fuse helium and re-expand into a red giant.
As others explained, our sun won’t explode. However it will become a red giant and become as large as the orbit of the Earth. (However, the earth will be pushed away, so it may or may not actually engulf the earth. Life as we know it on earth will still end, though).
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