Valence electron is an electron of an atom located in the outermost shell of the atom and can be transferred to or shared with another atom. It is most likely to be involved in a chemical reaction. These electrons belong to the highest value of the principle quantum number. Valence electrons are important in determining how the atom reacts chemically with other atoms. Atoms with valence electrons more than a closed shell (completely filled outermost shell) are highly reactive because the extra electrons are easily removed to form positive ions. Atoms with valence electrons fewer than a closed shell are also highly reactive because of a tendency either to gain the missing electrons and form negative ions, or to share electrons and form covalent bonds. Atoms with no valence electrons i.e. completely filled outer shell tend to be chemically inert.
Example:
Neon atom has 10 electrons with configuration 1s22s22p6. Its outer shell 2p is completely filled. It does not have any valence electrons. So it is chemically inert.
Magnesium has 12 electrons with electron configuration is 1s22s2p63s2, the valence electrons would be the 3s electrons i.e. 2 electrons.
Valency
Valency, also called valence, of an element is the number of electrons it needs to gain or lose to obtain a stable state (where the outermost shell is completely filled, chemically inert) . It also indicates the number of atoms of element that combine with number of atoms of other elements to form molecules of chemical compounds.
Sodium (Na) has 11 electrons with electrons arranged as 1s22s22p63s1. It means it has 1 valence electron. Chlorine (Cl) has 17 electrons with electron arrangement 1s22s22p63s23p5 which means it has 1 valence electron. So if sodium loses 1 electron it ends up with 10 electrons and if chlorine gains 1 electron it ends up with 18 electrons. This way both get their outermost shells completely filled and form a stable structure of sodium chloride (NaCl).
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