Why are valence electrons important?

In a word: !

are the outer electrons, and therefore they are the first ones to interact when two atoms come near each other. The bonding between the two atoms is due to the interaction of those . Whether they share them or give-or-take them, it is almost exclusively the electrical forces of the valence electrons that holds the atoms together.

Consider the noble gases. They don't generally do anything with their valence electrons. They don't share them, give them up, or receive any more, and as a result, the noble gases don't bond with anything.

Here is a video which discusses how to draw Lewis structures for atoms showing their number of valence electrons which are critical for determining how the atoms will bond with other atoms. Video from: Noel Pauller