The vertical columns in the periodic table are called groups. Each group contains elements that have similar properties, because they have the same number of Valence electrons.

Cool interactive periodic table

http://www.bbc.co.uk/education/guides/zsp4jxs/revision/7

Elements in the same horizontal row are in the same period.

http://www.bbc.co.uk/education/guides/zsp4jxs/revision/4

See Atomic structure

Development of the periodic table: "Law of Octaves", Mendeleev's periodic table

Some properties

Chemical elements and Chemical compounds