Question

What is the relation between valency of an element and the number of valence electrons in its atoms.?

Answer 1

the valency of an element is the number of atoms lost or gained by the atom of an element.
valence electrons are the number of electrons present in the outermost shell of an atom
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valency of an element depends on the valence electrons

valency of atoms having 1,2,3 valence electrons
= number of valence electrons

valency of atoms having 5,6,7 valence electrons
= 8 - number of valence electrons

Answer 2

Before knowing the relation let's take a quick peek into their definitions

Valency
It is the combining capacity of an element with the atoms of another element to form a chemical compound.
And who combines?
They are the electrons.

Valence Electrons
These are the electrons that combine with other atoms to form a chemical compound.These electrons are the ones that are present in outermost shell of  an element , and they only take part in forming new compounds not all the electrons.

So, the valency of an element is the number of valence electrons lost,gained or shared when forming a compound.An atom loses,gains or shares electrons so as to achieve the noble gas configuration.

For, example Na (sodium) , Cl (Chlorine)

Na has the electronic configuration --> 2,8,1
It has once valence electron, so this 1 electron takes part in reactions,hence this the valency of Na (+1).

Cl has the electronic configuration --> 2,8,7
It has 7 valence electrons, but it can't lose so many because it would involve a lot of energy, so it gains an electron.So, its valency is - 1.