Avertical column within the perioic table represents what ?

The columns, aslo caled a group, in chemical periodic system represent the number of valent electrons.

Valent electrons are electrons located in outermost electron shells, and they participating in forming of chemical bond. The old notaion of columns were greek numbers from I (1) to VII (7), representing the number of valent electrons, with exception of 0 (zero) for noble gases which have 8 valent electron. The modern numbering of a groups is recommended by the International Union of Pure and Applied Chemisty (IUPAC) starting from 1 to 18.