In their non-ionized form they differ only one proton and one electron from the nearest noble gas (in the Periodic Table).
The electron shells are built just the same as that of the adjoining noble gas, except it has one extra electron in the outer shell.
By getting rid of this one electron, the electrons left form a "noble gas" configuration, that is more stable. The alkali will become a positive ion by doing this, e.g.
The electron will be gladly accepted by e.g. a halogen, because these lack one electron as compared to the "noble gas" configuration:
This explains the reactivity of both the alkali metals and the halogens, especially if they are combined.