Tennyson (whether it's the real-life Tennyson or a fictionalized version is up for grabs) kicks things off with a prologue that evokes Jesus as a sort of muse. Our speaker seems hopeful that there is a reason for man's existence and a bigger plan for everyone. Humans are puny in comparison to God, and that's why people grieve so much. They just can't see the larger plan and can't get enough distance to put things like the loss of human life within a greater context.
The speaker gets right to some heavy-duty mourning over a close friend's death (who we later find out is named Arthur). He re-creates in his mind how his friend's body came back to England from Italy. Tennyson moves through various stages of grief, from "calm despair" to "wild and wandering cries." Even though he sometimes regards his feelings as sins, he defends them as normal.
Next, Tennyson meditates upon the comfort he can gain from the Bible and upon how various resurrections worked there. And no—he's not talking about literally raising Arthur from the dead. Instead, it's all about considering the idea of being immortal in a Christian sense (where the good guys get to go to Heaven). He he tries to take some comfort in that, but it's hard out here for a mourner.
So, he moves on to thinking about how nature fits in with The Big Picture. Tennyson starts to struggle with finding meaning in a world that seems random and governed by uncomfortably new ideas such as the Theory of Evolution (that reference to "Nature red in tooth and claw" is one big hint that this is very much on Tenny's radar). He also struggles with the idea that God is good when he has seemingly created a world filled with human suffering.
Tennyson finally takes comfort in the idea that humans, at least, are good—like his friend Arthur, who was intelligent and really cared about people. He considers some answers to problems he previously set up and, in what we might regard as the climax of the entire poem, imagines reuniting with Arthur. He starts to feel better and lets go of some of his doubt.
Toward the end, he starts to realize that it's all about gaining knowledge, and that knowledge is one of the higher purposes of humans. He also recognizes that human beings have souls, which allows for a sort of immortality. He ends with an epilogue that celebrates the wedding of his sister. So, Tennyson has lost a dear friend, but ends up gaining a brother-in-law whom he is hopeful might be a sort of stand-in for Arthur.