If someone is teetotal, or a teetotaller, it means they do not drink alcohol. Not at all; not even a little bit.
It appears the origin is from the word "total" as in total abstainer, with extra emphasis on the first "T". "T-Total"
According to http://www.uselessknowledge.com/word/teetotal.shtml,
It was first used in the sense of abstaining from alcohol at an 1833 temperance rally in England by a working man named Richard Turner.