The Dead Poets Society was an old, secret society at Welton—one which Mr. Keating was involved with back in his days as a student. What do we know about their super-secret activities? Well, we know they read poetry to each other and encouraged each other to "suck the marrow out of life"…which sounds downright disgusting, but is actually a super-good idea (even if you're not big on chowing down on bone marrow).
We also know they had official meetings, which were off-campus and—oh, yeah—not officially sanctioned.
But why did they call themselves the Dead Poets Society? Why not just call themselves the Poets Society? Isn't adding the "Dead" a little bit morbid?
The answer is yes, but it's morbid on purpose.
See, it's all about realizing their own mortality and the urgency of living life to the fullest while you're still alive to do so. When Mr. Keating first meets the boys, he takes them to see the pictures of the long-dead Welton alumni to remind them of the fleeting nature of life, and the importance of leaving a mark before life is over.
Reading the words of poets who have come before, and who left a verse or two behind, works as an inspiration for the boys. Those dead poets sure were insightful.