What is the form of the sonnet?

Sonnet 55 uses the form and structure that is now called the "Shakespearean" sonnet because of Shakespeare's use of it throughout his sonnet cycle. It differs from the Petrarchan sonnet form that was more commonly used at the time of Sonnet 55's writing. As with all sonnets, the poem has fourteen lines. However, its rhyme scheme differs from that of Petrarchan sonnets in a way which helps Shakespeare set up and execute the argument of the sonnet and then bring it to a conclusion in the closing two lines.
The rhyme scheme of the Shakespearean sonnet is ABAB CDCD EFEF GG. The rhyme scheme of a Petrarchan sonnet, by contrast, is ABBAABBA CDECDE. There are other sonnet types (see the link below). But perhaps the reason Shakespeare chose the form he did (which is named after him, but which he did not actually invent himself) is that it is a more appropriate vehicle for the points he wished to convey. In Sonnet 55, we can see how the structure with a rhyming couplet as the final two lines, using a different rhyme from all that have preceded it, helps isolate the "moral," or point, of the sonnet by emphasizing these lines:

So, till the Judgement that yourself arise,
You live in this, and dwell in lovers’ eyes.