The title sets up the joke: a "black thumb" is the opposite of a green one, the mark of someone who kills plants rather than coaxes them to grow. The two short lines then turn that failure into a kind of boast. The yard is so overgrown and foul ("rank") that even morning, which usually brings freshness and light, can't break through it. Then comes the speaker's cheerful vow: "I shall grow the dirtiest rose."
What stands out is the speaker's attitude. Instead of apologizing for the mess, they seem to accept it, even enjoy it. A rose is normally a symbol of beauty and care, so a "dirty" one feels both funny and a little defiant. The tone is wry and self-mocking, but there is something stubborn and hopeful in it too. The poem suggests that something can still bloom in neglected, unpromising ground, even if it doesn't look the way a rose is supposed to.