Why do atoms bond?

Atoms bond because they have an inherent need to have their outermost level of electrons be "full".

Some lose their electrons to eliminate a level of energy, at which point the new outer most level (the one underneath the one that removed) electrons do not occupy a level until the levels closes to the nucleus is are full.

At This point they are ionic. The other bonding element gains the losing atoms electrons.

This results in one atom being positively charged and the other negatively charged resulting in attraction between the two. (cations and anions, respectively).