Group
Definition
A vertical column of the periodic table. Elements in the same group behave similarly because they have the same number of outer electrons.
Technical definition
A group is a vertical column (numbered 1-18) of the periodic table containing elements with the same number of valence electrons and therefore similar chemical properties, such as the alkali metals in group 1 or the noble gases in group 18.
Example
Lithium, sodium, and potassium are all in group 1. Each has one valence electron and reacts vigorously with water.
Common confusion
Groups run top to bottom as columns, not left to right. The horizontal rows are periods.