A more 'noddy' description (a description without QM that would have satisfied a Victorian, perhaps) could be that each atom shares each electron. The attraction between each proton and each electron pulls the two protons together until their mutual repulsion balances out the attraction. This covalent bonding happens in many other molecules and describes how large molecules with chains of Carbon atoms (in particular) can exist. School Chemistry describes the bonding between some atoms of different elements as 'ionic bonding'. In that case the model is that one electron moves from one atom to the other and actually forms two ions. (Google it).
Also, Metals are held together very strongly because the outer electrons are shared by many adjacent atoms, (a form of covalent bonding, if you like). As the metal is stretched, the electrons keep pulling and they latch onto different atoms. So the metal doesn't break because other bonds are formed.