In short, transaction contracts are an attempt to conceptually unify different transaction flows that we do not want regular users to be bothered with. Users just need to understand that a transaction requires each party to sign the “transaction contract”, that’s all anyone needs to understand unless they want to know more.
Conceptually, any transaction can be seen as a transaction contract that requires those who send and those who receive coins to sign the transaction contract. It is combined with unified payment proofs (works for both SRS and RSR the same). Furthermore contract transaction flow is kind of a preparation for the future when perhaps multiparty transactions contracts (e.g. MultiSig) will become possible (currently not possible due to some complications when more than two parties are involved and payment proofs).
For further reading: