Apologies for not having completely strict and vetted sources – with the subject matter, that's kind of to be expected – but I'll include what I do have at the end. This was copied from Snopes, but basically verified by the rest of the sources.

[The 420] origins appear to lie in the escapades of a group of friends from San Rafael high school, northern California, in 1971. That autumn, the five teenagers came into possession of a hand-drawn map supposedly locating a marijuana crop at Point Reyes, north-west of San Francisco.

The friends — who called themselves the Waldos because they used to hang out by a wall — met after school, at 4:20 pm, and drove off on their treasure hunt. They never found the plot. "We were smoking a lot of weed at the time," says Dave Reddix or Waldo Dave, now a filmmaker. "Half the fun was just going looking for it." The group began using the term 420. So did friends and acquaintances, who included — at a couple of steps removed — members of the Grateful Dead rock band. The term spread among the band's fans, known as Deadheads.

Then in 1990 Steve Bloom, an editor at High Times, saw 420 explained on a Grateful Dead concert flyer. Staff on the magazine, long the leading publication on marijuana, started using it.

Sources:

http://www.snopes.com/language/stories/420.asp

http://www.hightimes.com/read/history-420

http://articles.latimes.com/2012/apr/20/nation/la-na-nn-pot-day-20120420

http://www.huffingtonpost.com/2013/04/20/420-weed-day-marijuana-april-holiday_n_3122359.html

Even if it's untrue, it seems that's the accepted answer these days.