Shaantam Shaashwatamaprameyam anagham Nirvaana-shaantipradamBrahma-shambhu-phanindra-sevyam anisham vedaanta-vedyam vibhumRaamaakhyam Jagadishwaram sura-gurum maayaa-manushyam HarimVandeham karunaakaram Raghuvaram bhupaala-choodaamanim
Word by word meaning
Shaantam -One who is in a state of Tranquility.Tranquility means peacefulness,the ultimate peace or experience of our own mind merging with bliss or feeling bliss
Shaashwatam- means eternal
Aprameyam -Inexplicable or one who cannot be explained or one who cannot be introduced in words.Beyond all words and beyond all explanation
Anagham - One who is immaculate or without blemish.One who may not have any mistake to commit.
Nirvaana-shaantipradam -One who blesses with bliss
Brahma-The Lord of creation.One of the trinities.
Shambhu -Shiva ,the lord of dissolution.
Phanindra - The Serpent King,Ananda or Sesha
Sevyam - One who is served upon.
Vedaanta - vedyam -One who is known through Vedaanta or Upanishads
Vibhum - All pervading or omnipresent ,The strongest or Omnipotent and one who knows everything or omniscient.
Raamaakhyam - One who is well known as Rama or one who is inspiring and illuminating everything in the form of Soul.
Jagadishwara - Lord of the whole Cosmos
Sura- guru - The preceptor of the Devas
Maayaa - manushyam- A person who has veiled himself with his own delusions or one who creates all delusions;
Hari -One who attracts the minds of the devotees in the form of Vishnu or one who absorbs the sins of all
Vandeham - I salute,pay homage to,pay respect to
Karunaakaram -Ocean of compassion.
Raghuvaram -The noblest in Raghu's Dynasty.
Bhupaala - choodaamanim- One who is glittering as the diadem of all kings.
Thus the stanza means
I pay homage to the one who is eternal ,tranquil,immaculate, inexplicable with words and who blesses with bliss .I salute the omnipresent ,the omnipotent and omniscient one well known as Rama who is always served upon by the Lords of Creation and Destruction as well as by the serpent King Sesha. I pay respect to The Lord of all Cosmos, The preceptor of the Devas and ocean of compassion, who is known through upanishads and has veiled himself with his own delusions. I prostrate before the noblest in Raghu's Dynasty who glitters as the diadem of all kings and who absorbs the sins of all
Sundar Kand Sree Ram Sloka Meaning taken from the speech of Jagadguru Swami Sathyananda Saraswathi Tiruvadikal. Listen to the concept in Swamiji's own words below