We introduce an intriguing new type of argument systems with the additional property of being explainable. Intuitively by explainable, we mean that given any argument under a statement, and any witness, we can produce the random coins for which the Prove algorithm outputs the same bits of the argument. This work aims at introducing the foundations for the interactive as well as the non-interactive setting. We show how to build explainable arguments from witness encryption and indistinguishability obfuscation. Finally, we show applications of explainable arguments. Notably, we construct deniable chosen-ciphertext secure encryption. Previous deniable encryption scheme achieved only chosen plaintext security.