There is a belief that it is a code used by the police to describe an offence in progress, saying something like "We have a 4:20 in progress", meaning someone or people are smoking pot. Generally, potheads or stoners will refer to smoking pot at any time as 4:20. 4:20 on April 20th is the ultimate4:20 of the year.
Hey dude, what time is it? 4:20 man.
(the time could be 9:45, but sincethey are smoking a joint it is 4:20)