Why is space black if there are so many stars?

If the universe were infinite, eternal, and evenly filled with stars, every line of sight would eventually land on a star's surface and the night sky would blaze in every direction. It does not, and that contradiction is famous enough to have a name, Olbers' paradox. The resolution is that the universe is not eternal. It has a finite age, roughly 13.8 billion years, so light from objects beyond a certain distance simply has not had time to reach us, leaving genuine gaps of darkness between the stars we can see.

Expansion does the rest. Space itself has been stretching, which stretches the light traveling through it toward longer wavelengths, a redshift that pushes the oldest and most distant light out of the visible range entirely. The sky is not actually empty in those directions: the cosmic microwave background, the leftover glow of the early universe, fills the whole sky, but stretched by expansion into microwaves your eyes cannot detect. Point a radio telescope anywhere and it is there. So space looks black because of the universe's finite age and its expansion, not because there is nothing out there, and the darkness of the night sky is itself evidence for the Big Bang.