This "story" is about the narrator getting angry with an enemy. He keeps the anger to himself, allowing it to get more and more intense. He lets is "grow" inside his body. Symbolically, he plants a tree of his anger in his garden, and it grows to bear an apple. In the story, the enemy eats the apple and it kills him. The connection is that the narrator's anger has born a deadly fruit that will have negative - even murderous - consequences on his enemy.
Blake is trying to show how dangerous wrath can be. The wrath the narrator has towards his friend is spoken of and quickly disappears. This is what is supposed to happen. However, the wrath towards the enemy does not get released, and it brings with it much negativity. The idea that the wrath brings forth a poison apple is symbolic of the Garden of Eden. It was human sin in the garden that caused Eve to eat the apple and get her and Adam kicked out of the Garden. Blake uses the apple to suggest that wrath/anger is a sin and needs to be put aside, not let to grow.
The narrator isn't the only guilty party, however. The enemy also sins:
And my foe beheld it shine,
And he knew that it was mine,
And into my garden stole
Here, it is the sin of "coveting" that causes the enemy to want what is the neighbor's. By taking it, he is just as guilty in his own death, and proves again that humans share original sin.
In 1794, Blake published his "Songs of Innocence" and "Songs of Experience" together as "showing the two contrary states of the human soul."
"A Poison Tree," is a song of experience and its theme is 'hatred.'
Enemity with his "foe" prevents the persona of the poem from having a heart to heart conversation with him and putting an end to all misunderstanding and thus getting rid of his anger. Consequently, his anger becomes a full fledged grudge which finally bears fruit as a "bright apple."
The literal meaning: The "bright apple" has been "poisoned" by the speaker's anger and hatred. His enemy is tempted by this bright fruit and he surreptitiously bites into this 'poisoned' fruit and meets his tragic end which makes the speaker 'glad.'
The symbolic meaning: The tree represents the Tree of Knowledge in Genesis ch.2. Adam and Eve were 'fobidden' to eat the fruit of this tree because then they would know the difference between 'good' and 'evil' -they would permanently lose their 'innocence.' Since, the speaker does not talk to his enemy, the enemy fails to understand the intensity of the speaker's hatred and he is tempted to clear up the misunderstanding and becoming friends with him. He is deceived by the hypocritical behaviour of the poet speaker and his attempt at reconcilement is rebuffed and only ends in the death of his 'innocence' which makes the speaker happy.