Question

Why do atoms gain, lose, or share electrons?

Answer 1

Atoms gain, lose, or share electrons to gain a full outer, valence shell. Since most atoms have an outer shell that isn't completely full, they will bond with other atoms or ions to gain a full valence shell. 

(Side note: This is why noble gases do not bond; they already have a complete valence shell.)

Hope this helps!

Answer 2

They do this in order to become more stable.
Hope this helps :).