What do elements in the same column in the periodic name have in common?
Short answer they have the same amount of outermost electrons and hence similar chemical properties.
Atoms in column 1 (H, Li and Na for example) have 1 valence electron.
Column 2 have 2 valence electrons, 13 have 3, 14 have 4 and so on.
An atom can have at a maximum 8 valence electrons (this becomes a bit more complicated after the third row). And the "goal" of an atom is to have its outermost electron filled (either by emptying the outermost shell making the filled, second outermost shell the outermost or by filling the outermost shell).
This affects which charge ion of the columns produce
Column 1 produce 1+, column 2 2+, column 13 3+, column 15 3-, column 16 2- and column 17 1-.
The column of the atom also affect the amount of bonds an atom can participate in but this is not as simple.