The number twelve is significant, of course, in that it's the number of people who serve on a jury. So we know from the get-go that this is probably going to be some kind of courtroom drama.
To be fair, not all twelve men in this movie are angry—at least not all at the same time. But the title screams "Conflict!" and tells the audience that there are at least twelve personalities who could affect the outcome of the plot. Chances are that screenplay writer Reginald Rose chose the title because it suggests action and suspense. At least that's how this old movie poster tries to spin it.