Alyosha is so good, so pure, that next to the other characters in the novel, he seems to have no personality at all. All the other characters – from Fyodor and the other Karamazov brothers, down to the most insignificant child – have their own distinctive voices and flaws, but it seems like Alyosha never says a word of his own.
And yet, if Dostoevsky's preface is to be believed, Alyosha is supposed to be the central hero of the novel, as well as the sequel that Dostoevsky never lived to write. Dostoevsky sounds almost apologetic in his preface: "To me [Alyosha] is noteworthy," he explains, "but I decidedly doubt that I shall succeed in proving it to the reader. The thing is that he does, perhaps, make a figure, but a figure of an indefinite, indeterminate sort."
So how does an "indefinite, indeterminate sort" end up the hero of one of the greatest novels of all time?
Well, as the antithesis of what we expect from a hero, apparently. Alyosha embodies the opposite of what the world values: he doesn't have the swashbuckling bravado of Dmitri, or Ivan's intellectual brilliance, or his father's enormous wealth. Poor and humble, yet with a fresh-faced demeanor, Alyosha spontaneously inspires love in everybody around him because everyone responds to his open, loving, and good nature.
The narrator calls Alyosha a "lover of mankind," and the novel sets up a lot of parallels that hint at Alyosha's divine gift. Like the Christ in Ivan's "Grand Inquisitor" parable, Alyosha is largely silent. But it's because he is silent that, unlike the other characters, Alyosha is a really good listener. Conveniently, this makes Alyosha a great character to knit the various storylines together. Instead of abruptly moving from scene to scene, Dostoevsky has us follow Alyosha around town, where everyone seems to want to unburden their deepest, darkest secrets and desires to him. The novel has a different feel, a frantic pace, when Dostoevsky has us follow Dmitri around in Book 8.
When Alyosha does speak, he speaks the pure, simple truth. Because of that, he doesn't get huge, rambling monologues, like many of the more troubled characters.
Alyosha's canny simplicity, and its effect on the other characters, bears out Zosima's claim that the simple wisdom of Biblical stories can move us to do good if we only open our hearts to their words (6.2.b). Speaking the truth to characters who are so self-deluded by their own pride is nothing short of shocking. When Alyosha abruptly declares that Ivan and Katerina love each other, for example, both are so bewildered that Ivan runs off and Katerina goes off into hysterics (4.5.30).
This isn't to say that Alyosha is immune to doubts and fears. His faith is certainly tested. Perhaps his low point is the death of the elder Zosima. When the elder's corpse stinks instead of miraculously smelling of flowers (proving he was only human, not a saint), Alyosha's faith is turned upside down.
This moment of despair, however, only strengthens his faith. Moved by Grushenka's kind gesture (her refusal to seduce him), Alyosha realizes his fault: he was expecting a miracle to confirm his elder's saintly status. This desire, which is essentially an idolatrous one, goes against everything the elder preached about humility, about finding God's grace in everyone, including someone as unlikely as the seductress Grushenka. As his mystical experience back at the monastery (in the Marriage in Cana chapter) confirms, Alyosha's painful disappointment turns to a renewed faith, which prepares him to go out into the world and serve his fellow man.
Alyosha is thus Dostoevsky's response to Ivan's devil, who described himself as the "x in an indeterminate equation" (11.9.7). The devil suggests that without him to serve as the engine of human suffering there would be no history, no struggle, no human sin, and thus no need for God. By making Alyosha an "indeterminate" figure, the novel implies that it is the love of God, rather than evil, that is the real force that moves the world and human hearts.
So, yes, Alyosha doesn't say much. Perhaps it would be more fitting to call him an image rather than a full-fledged character – or perhaps he's both. The elder Zosima made much of Alyosha's "brotherly countenance," even noting his resemblance to his (Zosima's) dead brother (6.2.a). The simple but moving power of Alyosha's brotherly countenance reminds those around him that they are not alone, that someone shares a brotherly interest in their suffering and, perhaps, may offer a way to happiness, which is only possible through the work of love.