When a teacher asks for an analysis of the theme and structure of a poem what sort of answer is expected?

There are several topics you should cover in an essay
analysing a poem. The first is prosodic structure. What is the basic metrical structure
of the poetic lines  (if the poem is not in free verse)? One the level of line, you need
to specify type of foot (iambic, dactylic, etc.) and number of feet per line
(tetrameter, pentameter, hexameter, etc.) if the poem has a regular metrical structure.
On the stanzaic level, you need to use the standard terms to describe the large scale
rhyme scheme of the poems. In some cases, this will involve a scheme repeated over
multiple stanzss (terza rima, heroic couplet, open quatrain) and in other a unique
overall patterning (Italian or English sonnet) or pattern of repitition of lines
(rondeau, villanelle).

Next you need to note the type or
genre of poem -- is it comic? epic? mock epic? narrative? -- and which specific period
and school it falls into (metaphysical? imagist? symbolist? modernist?) Next you need to
consider the major topics covered in the poem and its dominant mood. Also consider the
narrative voice of the poem and its relationship to the subject
matter.