Valence electrons are quite important. They are the electrons that exist in the outermost shell/cloud of an atom at the highest energy level. When atoms interact chemically through bonding, it's their outer shell electrons that are involved. The number of outer shell or valence electrons influences how the element will react by gaining or losing electrons to create stability. The periodic table of elements is arranged to reflect this. Elements with the same number of valence electrons are in the same column. The less valence electrons an atom holds, the less stable it is.
Electron configurations tell us how many valence electrons are in an element and therefore give us an idea of the element's bonding ability, magnetism, and other chemical properties.
As an example, calcium is element #20. It is in the fourth period in the second column of the s block. Therefore calcium has an outermost electron configuration of 4s^2.