Valence electrons is the name given to the outermost electrons of any given element. Every element has from one to eight valence electrons and they determine how the element will combine in chemical reactions with other elements. When elements react with other elements in ionic reactions they will generally gain or lose electrons to minimize the number of electrons moving from one element to the other.
Metals - those elements to the left of the stairstep elements on the periodic table - generally have 1-3 valence electrons while non-metals generally have 5-7 valence electrons. This explains why, when metals react with non-metals that the metals lose their valence electrons to become positive cations while the non-metals gain valence electrons to become negative anions. This is called the octet rule and says all elements are most stable when they have a full number of valence electrons. For all but a handful of elements that number is eight - hence the "octet" rule.
In the periodic table the elements are arranged in groups or families based on the number of valence electrons the element has because that number identifies elements with similar properties.
The octet rule also explains why the group 18 elements (the noble gases) do not react. Since they already have a full outer shell of electrons, it takes a large amount of energy to remove one of their valence electrons and would add a large amount of energy of one more valence electron was added.