What a broad question! There are many different characteristics of poetry. The characteristics change based upon the period from which the poet comes from, the form the poet chooses to write in, the poetic/literary devices the poet chooses to use, and the rhyme or meter the poet chooses to depict.
Depending upon what genre you are looking at, one poet within a movement can differ greatly from another. Not only do poets within a movement differ, poets in different genres differ greatly as well.
That being said, there are some characteristics that are typical to many poems.
Poetic devices- Many poets use poetic devices within their texts. Common devices used are:
1. Alliteration- the repetition of a consonant sound within a line of poetry. Creates a sing-song affect which allows the words of the poem to roll off the tongue more smoothly.
2. Assonance- the repetition of a vowel sound within a line of poetry. Like alliteration, this devices provides a softening to the line or harshness depending upon the vowel repeated.
3. Metaphor- the comparison of two or more things one would not necessarily use to describe the other. The use of metaphors allows poets to make comparisons that readers would not normally make. This allows readers to expand their minds and look at simple (or elaborate) objects in a different way.
Poems also have specific moods. A mood is what an poet embeds in the text so as to evoke a specific feeling from the reader.
Many poems also have a specific theme. A theme is the subject of the poem. Examples are racism, love, hate, stereotypes, and fear (to name a few).
Some poets use specific forms to write in (such as iambic pentameter or couplets). While others choose to use free verse with no rules.
Basically, poetry can be as precise or as open as the poet wishes. Defined characteristics for all poetry simply do not exist given all poets are different and write in different ways.