What is the poison tree inside us?

The "poison tree" you ask about is the central image in William Blake's poem "A Poison Tree." In that poem, the narrator gets angry with a friend. After he becomes angry, he does not let the anger pass. Instead, he feeds it with fear, crying, and deception. It blossoms into an apple that appears lovely, but in reality, is poisonous. That poisonous fruit kills his former friend.
The poison tree is what becomes of your soul when you feed it with negativity. By implication, your soul could become a positive and nutritious element of your being if you fed it with love, confidence, and honesty. The poison tree is a soul that has been fed with all the violent, corrosive emotions people feel. A poison tree is an angry, deceptive, hurtful soul (that doesn't have to be that way).