"In memoriam" is fancy-pants Latin for "in memory of [insert dead person's name here]." So, we're basically talking about an obituary, folks. The poem's speaker is experiencing the various stages of grief and trying to juggle his sense of loss with his religious faith.
Tennyson wrote his most famous poem in memory of his close friend, Arthur Henry Hallam, who died at the tragically young age of 22 in 1833. (Sometimes you'll see the title as In Memoriam A.H.H.)
The work was almost named either Fragments of an Elegy (pretentious) or The Way of the Soul, which really does bring out the angst-y, struggling-with-loss-in-a-senseless-world feeling of the piece. Interestingly enough, the final title was suggested by Tennyson's fiancée, Emily Sellwood (so score one for the ladies) (source).