Shit happens is a common vulgar slang phrase, used as a simple existential observation that life is full of unpredictable events, either "Así es la vida" or "C'est la vie". The phrase is an acknowledgment that bad things happen to people seemingly for no particular reason. The phrase was first observed in 1964, but wasn't used in a print publication until 1983. Alternately said, albeit less vulgarly, as "stuff happens". A possible origin is "it happens", which rhymes with it.
History
The fact that people have been remarking that shit happens has been attested from 1964, when Carl Werthman quoted an example in his UCB MA thesis; the relevant excerpt was published in The American City (edited by Anselm L. Strauss) in 1968.
In a review of Fred Shapiro's 2006 work The Yale Book of Quotations, The New Yorker critic Louis Menand stated that it is "extremely interesting" that the phrase "Shit happens" was introduced to print by Connie Eble, in a publication identified as UNC–CH Slang in 1983.
The phrase is also spoken by Forrest Gump with a short discussion of what it means in the movie (1994) by that name starring Tom Hanks.