They’re so bright because they produce so much energy every second!
Stars generate power by fusing hydrogen atoms together in their core. This process of fusing hydrogen is the most powerful process that we know. The Sun, for example, produces 384,600,000,000,000,000,000,000,000 watts. To put that in perspective, this is the equivalent of about 91,920,000,000 megatons of TNT per second, or 1,820,000,000 Tsar Bombas (which is the most powerful bomb we’ve ever built). The light bulb in the room your sitting in probably only about 60 W!!
Humans normally have a power requirement of 12,000,000,000,000 watts. That is significantly lower than the power output of the Sun – so if we could harness all of the power of the Sun, we could power the Earth without fossil fuels! (This is called building a Dyson Sphere https://en.wikipedia.org/wiki/Dyson_sphere).
So stars that are really far away are still visible to us because they are producing so much energy!
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