why do ions form?

Answer 1

A positive ion forms when an atom gives up one or more electrons.
It gives up the electrons because another atom "wants" them more.
In other words, the strength with which the first atom is holding the electrons is not as great as the strength with which the receiving atom is attracting them.

For any particular atom, there is a specific amount of energy required to "steal" each of its electrons. For Group I metals, this energy is very low, and they are easily ionized.

The other type of ion is a negative ion, which has acquired additional electrons to give it a negative charge. Again, there is an energy exchange associated with this ionization process, and the ionization will occur if the atoms that are present and the energies of ionization are such that the electron exchange allows the release of energy, or the reduction of a stress (such as pressure, temperature, or the density of the reactants).

Answer 2

Why do atoms form ions?

Atoms would like to be stable (meaning having a stable electronic configuration like noble gases, with a fully occupied outermost shell) and the way to do that is to give away their valence electrons (for metals) or to accept more electrons into their outermost shell (for non-metals).
When an atom start giving or taking in electrons, they longer have the same numbers of positively-charged protons and negatively-charged electrons, meaning they are no longer electrically neutral. Thus the atoms become charged and are called ions.
Hope this helps. :)