Abu Hurayrah (may Allah be pleased with him) reported that the Prophet (may Allah's peace and blessings be upon him) said: "None of you should offer prayer in a single garment that does not cover the shoulders."
It is required from the praying person to be in the best appearance while praying, as Allah, the Almighty, has mentioned in the Qur'an: {O children of Adam, take your adornments in every mosque}. Since meeting the kings, nobles, and honorable people necessitates being in the best appearance, so how about meeting Allah who is the King of Kings and Master of Masters?! For this reason the Prophet (may Allah's peace and blessings be upon him) encouraged the praying person not to pray with his shoulders exposed, while having something to cover them, or one of them. He prohibited praying in this state, while standing in front of Allah invoking Him.