Let's get this one out of the way right up front, shall we? In Memoriam's very title drops a big clue on our heads that we're dealing with grief and mourning. In memoriam means "in the memory of" someone who has passed away. We soon find out that this is Tennyson's close friend, Arthur.
The entire poem is devoted to how Tennyson, over several years (we think...the chronology gets a bit funky), comes to terms with his grief. A major turning point comes when he famously acknowledges that "'Tis better to have loved and lost / than never to have loved at all" (567-568 and 1595-1596—it's so good he's repeating himself).
All of the over-the-top grief is a bit excessive. It's years later, so Tennyson should just get over it already.
In Memoriam is a fitting verbal resting place for Tennyson's dear friend.
Since Tennyson brings up The Big Guy immediately in the prologue of In Memoriam, we know right away that religion will be on the menu throughout the entire poem. This plays out in several different ways. Tennyson is struggling to make sense of the world and his faith after suffering the loss of his friend. Things just don't make sense like they used to.
He's also struggling against his faith because of nineteenth-century scientific discoveries, like the Theory of Evolution (check out "Themes: Man and the Natural World" for more info on that). Finally, Tennyson is also trying to "justify the ways of God to man," similar to what Milton does in Paradise Lost. If you're a fan of big technical words, that's called "theodicy." (Actually, it's called "theodicy" even if you aren't a fan of big technical words.)
Rediscovering his faith completely solves the speaker's anxiety regarding The Big Picture.
Tennyson ultimately acknowledges that there is immortality, which seems to justify the suffering that God allows in the world.
Here's a fun fact: Tennyson was probably the first English poet to tackle the problem of man's role in a universe that was (at the time) starting to be explained more and more by science (source). The Victorian period, during which time Tennyson lived, was the first period to have to face the implications of Darwin's Theory of Evolution.
As you can imagine, many people could just not deal with the idea that humans—supposedly the highest form of life and created in God's image—evolved from lower life forms. In Memoriam presents some of this anxiety, perhaps most famously in the nature "red in tooth and claw" verse.
Similar to the Romantic poets, Tennyson uses images of nature to show his interior states.
Tennyson presents nature as mostly a Big, Bad Force that is antagonistic toward humans. Even Darwin's newly-emerging theory is presented in negative terms.
Something that Tennyson continually runs up against in In Memoriam is his inability to adequately express what he's thinking or feeling. In some ways, this is right on, since he's dealing with lots of difficult concepts: grief, religion, man's place in the universe—oh my! But in another way, this is frankly total bunk. We all know Tennyson is the bomb when it comes to using words. He wouldn't have been made Poet Laureate of England if that weren't the case. So this anxiety about expressing himself is also just a pose to get us to reflect on the natures of words, language, and communication themselves.
This whole having-problems-expressing-himself thing in the poem is just a cheap ploy. Tennyson is trolling for compliments.
When words most break down in the poem are the places where we can see the speaker struggling the most with his grief and anxiety.