Valency is the combining capacity of the atoms of elements, that is, their tendency to react and form molecules with atoms of the same or different elements. This is done by sharing, gaining or losing electrons. Take the example of silicon. The atomic number of silicon is 14 so its electronic configuration is 2,8,4. It's outermost shell either loose or gain 4 electrons to attain the stable stable. Thus, the valency of silicon is 4. In another example of oxygen, its atomic number is 8 so its electronic configuration is 2, 6. It's outermost shell will gain 2 electrons to complete its octet. Therefore, its valency is -2.

Some of the learners also asked:
What are K and L shells?