Is the form of a poem the way the poem looks the way it is structured?

Form in a poem works any way the poet wants it to work (if the poet is skillful enough).

Many poets use form as a simple mnemonic device. A main reason why Shakespeare wrote in Iambic Pentameter is because verselines are easier to memorise than prose speeches. Shakespeare's actors needed to memorise many lines for each performance, having the play in verse makes this easier.

A poet like Spenser will use the form as a hypnotic, even soporific, technique. In the Faerie Queene the lines are often so melodious (Spenser reinforces his complex rimescheme with heavy doses of assonance and alliteration) that we let go and drift with the story. Since the story of the Faerie Queene is basically preposterous, it is a good thing if we aren't paying too much attention most of the time.

On the other hand, a sonnet writer often uses his form to heighten his reader's perception. Once we realise that there is a sonnet coming, we know that there will be only fourteen lines, and that there is very likely a stinger at the end. Shakespeare uses the sonnet this way in Romeo and Juliet, and Gerard Manley Hopkins teases his readers by launching big ideas that we know will not be fully explored (there is insufficient time).

Or form can be used as a conjuror's sleight of hand. In Byron's Don Juan there are some very challenging, even revolutionary, ideas. But Byron displays so much virtuosity and panache in his deliberately difficult choice of stanza and rimepattern that we notice how clever the poetry is, while the dangerous ideas slowly seep into our mind while we aren't looking.

I can carry on like this for hours - but by now you know enough to do your own researching.