A lot of what we recite in Salah 5 times a day has some interesting history or associated actions with it. For example, everytime we say, "sami Allahu liman hamida", it's the angels that respond, "rabbana lakal hamd". The translations of both being: Verily Allah listens to one who praises Him. Oh our Lord, all praises be to you.
In the second and fourth rakahs (or third in Maghrib), the tashahhud is a recreation of the conversation held between Allah and the Prophet Muhammad (peace and blessing upon him) during the night of the Heavenly Ascent (Miraj).
Attahiyyatu lillahi was salawatu wattay yibatu
Assalamu 'alayka ayyuhan nabiyyu
wa rahma tullahi wa barakatuhu
As-salamu 'alayna wa'ala 'ibadilla his saliheen
Ash hadu alla ilaha illal lahu
wa ash hadu an-na Muhammadan
'abduhu wa rasuluh.
All compliments, all physical prayer,
and all monitary worship are for Allah.
Peace be upon you, Oh Prophet,
and Allah's mercy and blesings.
Peace be on us and on all righteous slaves of Allah.
I bear witness that no one is worthy of worship except Allah
And I bear witness that Muhammad is His slave and Messenger.
And when we say the final salam over our right and left shoulders, we're actually saying salam to the angels, Kiraman Katibeen.
By being conscious of the history of our Salah, we can make it come alive, and add to the beautiful experience of submitting to our Lord.