It's means it's very "over" or brings out the feeling of watching a drama. It can also mean that's it's very moving or effective. For example,
"When Sophia cut her finger she was so dramatic! I thoght she'd faint."
In terms of a poem, it means that it's got a lot of wild feelings. If you're saying a poem is dramatic it means that you're saying it's got vast imagery, and effect on the reader in which it stirs emotions.
In short, it brings forth a lot of emotions.
"They laid the dead man in the dirt,
And all his happiness and hurt,
Faded away that day as one,
Despite which one on earth had won,
His hate and passions, loves and fears,
Gone as the eternal sleep nears,
All his quests and goals are now dead,
O the sorrows of the life's bed,
What is left of this young man?
Nothing, he is no more in the land"
No credit to me.
I hope I helped you some how.