What is a Sonnet?
For a full answer, the Wikipedia entry is probably as good a place as any to start.
But you may like to have the answer in, well, sonnet form. See 'What's a Sonnet, Miss?'
The Sonnet is only a form, after all, a structure. The fact that something is a sonnet says very little about the content of the poem. Sonnets have been used for both serious and light-hearted themes. Because they are relatively short, they aren't used to tell stories. There is really only space to make a single point and give some examples. If you try writing a sonnet you'll see what I mean.
Many sonnets present a main point or theme in the first eight lines and then clarify it or even contradict it in the final six lines. It's as if there is an "Ah, but..." at the beginning of the ninth line. This is something to look out for rather than a rule.
In terms of form, the sonnet written in English is (with a few notable exceptions - e.g. Hopkins) 14 lines long. It is most commonly written in iambic pentameter and has a clear rhyme scheme.
The rhyme scheme can vary from the very rigid to the somewhat relaxed! Most pre-20th century sonnets are fairly rigid in their schemes. Given the pressure this puts on certain line endings, it's amazing that so many fine sonnets were written with such seeming ease and grace.
Keats, Wordsworth and many others used the pattern ABBAABBA CDCDCD - just four rhymes for the whole poem - and managed to achieve that without the rhymes seeming strained.