Let us not forget that the reasons for human actions are usually incalculably more complex and diverse than we tend to explain them later, and are seldom clearly manifest. Sometimes it is best for the narrator to limit himself to a simple account of events.
When you really get down to it, the plot of this story amounts to nothing more than a soap opera, full of love triangles, unscrupulous people, and deceit. But the plot is really not what drives this novel. It is driven by its complex characters, lead by Prince Myshkin. The novel, which is written from the perspective of someone who knows about the story but wasn't a part of it -- an omniscient narrator -- opens with Myshkin returning to Russia from a long stay at a Swiss sanitarium. He has epileptic seizures (although this does not become apparent until much later in the novel) and there is a childlike simplicity to his interactions with others. This causes people to view him as a simpleton, thus giving the novel its name.
After he arrives in Petersburg, Myshkin looks up some distant relatives of his who usher him into the social circles of the city. Myshkin meets and falls in love with Natasya Filippovna, who very well may have more problems than the prince. He admits to some of those that he is close to that his feeling for Natasya are closer to pity than to love. In turn, she vacillates between wanting to be betrothed and physically fleeing from Myshkin (a la Runaway Bride). During this time, Myshkin corresponds with Aglaya, another unconventional young woman, who seems to have genuine feelings for the prince, but cannot come to terms with his mental state. More accurately, she is concerned what people will think.
A word about the Myshkin's mental state... Other than epilepsy, Myskin appears to have no extreme mental problems. Unusual candor and a propensity to speak from his heart are his big "problems." He is able to intelligently discuss current events, Russian history, literature, and debate philosophy. He does not abide by the social mores of Petersburg and speaks his mind, regardless of whether or not his opinions are popular. This is shocking to people who are supremely concerned with how they appear to others (most of the people Myshkin interacts with can be described in this way).
Amongst the many characters that surround the prince, there are two who are noteworthy: the nihilist Ippolit and the cad Rogozhin. What makes these characters important is that they bear some similarities to Myshkin. These three men start with the same basic beliefs, but each take a completely different philosophical path. As a result, they approach life in three very different ways. Some readers have asserted that Rogozhin and Ippolit represent the two ends of the spectrum of Myshkin's personality. While this is an interesting idea, I think is a bit of stretch to read this into the novel.
Others have described Myshkin as a Christ figure. I saw this in numerous places throughout the novel. Indeed, he is innocent and good to a fault. Whether the Christ analogy holds water or not, Dostoevsky uses Myshkin to address philosophy, religion, and the nature of Christ. With all these complex themes, The Idiot is firstly a novel of ideas.
Since Tolstoy is the only other Russian writer that I know much about, and since Tolstoy and Dostoevsky wrote during the same time, I feel compelled to compare the two. From what I have read, I like Tolstoy's writing better then Dostoevsky's. There. Comparison done.