How does the theme of "A Poison Tree" convey the poem's message?

The theme of "A Poison Tree" examines the detrimental effects of harboring anger. In this poem, the speaker is angry twice: once at a friend and once at a foe. When he's angry with his friend, they talk it out; his anger thus dissipates. In contrast, when he's angry with his enemy, he holds it inside. The anger grows into "wrath." This connotes a more powerful form of anger. A common term is a "wrath of vengeance." When anger reaches this level, people seek revenge. The speaker nurtures this anger, allowing it to grow until it becomes a symbolic apple.
The speaker's foe tries to steal from him and ends up eating his anger-filled apple. When it kills him, the speaker is "glad" to see him stretched out beneath the tree.
The overall meaning here is that the speaker has now become something he never intended to be. His heart is so hardened by the anger he has allowed to grow that he doesn't care about the devastation he has caused; in fact, the pain of his foe brings him happiness.
So who wins here? Not the foe, and not the speaker. Living in anger causes unforeseen consequences to one's character.

The theme of "A Poison Tree" is its message. The theme/message Blake is communicating in this poem is that it causes damage to hang onto a hurt. If somebody hurts or upsets you, the best path to getting over it is to talk to them about it as quickly as you can. That way, you can get the problem resolved and move on with your life instead of ending up up doing something hateful. Resolving an issue occurs in the first two lines of the poem, when the speaker works out a problem with a friend. The speaker states:

I was angry with my friend;
I told my wrath, my wrath did end.

The rest of the poem, however, describes how the speaker holds onto to his anger against an enemy. Because he does this, the anger grows and grows. The speaker pretends to like his enemy, smiling as if everything is fine, but inside he is creating emotional poison—a toxic environment of hate—that Blake visualizes as a poisoned apple.
The speaker eventually kills his enemy with his hate and is glad of it. Blake thus shows how holding on to hurts can turn us into people who enjoy destroying others.