"The sun" is what we call the big ball of fire up in the sky. It's almost always "the sun", not "a sun". There's only one of them, and everyone knows which sun you're talking about, so we use "the" before "sun".
But you may also hear people using "sun" in other ways. For example:
This means that the listener's skin is tanned or maybe burned a little bit.
In this example, "all that sun" means "all that sunlight that they were exposed to".
I could use a little sun.
When people use "sun" in this way, they're really talking about the light from the sun, or the effects of the sun on a person's skin.