saNtataM chiNtayEnaNtaM aNtakAlE vishEShataH

naivOdApurgRuNaNtOMtaM yadguNAnAmajAdayaH |

saNtataM = Always; even during pralaya when all other jeevas are asleep. At this time only Brahma and Vaayu are aware about Paramaathma.

chiNtay+Ena+aNtaM = Enam means Narayana/ swami to all.

aNta+kAlE = when death is near (for common man); For Vaayu and Brahma during paralaya.

Bhishma always contemplated God and near to death he also composed “Bhishmastavaraja” but when dying he couldn’t remember God.

naivOd+Apu+urgRuNaMtO+aNtaM yadguNAn+Amaj+AdayaH =

“Aja” means one who doesn’t have birth. “Aja” also means one who took birth from Narayana – Brahma.

Ugrunantam = remembering during day and night during paralaya too and still can’t contemplate all the Gunas of Narayana.

Vishnu suktha says “nathe Vishnu jayamanaha na jataha devam mahimanaparam antha mavap” that is “Nobody born now or born before is aware of all gunas of Narayana.”

Brahma and other great gods praise the unique, great and extraordinary auspicious qualities of the Lord of all who has no end (of the four kinds) and can never reach the position of having completely described or understood even one of these qualities. I will contemplate such a Paramaathma always.

This sthothra is an aid to remember the extraordinary qualities of the Lord and also serves as an Aaapadashira sthothra – describing Him from feet to the Head.

Vasudeva (the prelude to the Krishna Icon being installed shortly) is the fittest entity to be worshipped as He is Himself without blemish and is the giver of boons to boon givers themselves. More over, He is the only person who can give Moksha, which none else can give and gives this supreme blessing even to the others. The conviction that  Krishna is supreme, without blemish and can give us the greatest gift which we can aspire, will lead to our praying Him  rather than any one else and will also make us disinterested in worldly boons – just as some one who has access  to the emperor will not seek some minor favours from a lesser official. The prayer also conveys the nature of the true Rju Jiva – absolute certainty in knowledge, devotion to God Vishnu surpassing all else and being never affected by  ignorance (Ajnana). The sthothra also conveys the following qualities of Vishnu :

1. His Sakala Kalyana Guna paripoornathva
2. His Nirdoshathva
3. His supremacy over all other gods
4. His grace being essential for the removal of primordial ignorance (Ajnana)
5. His being served by His consort Lakshmi – in every manner possible.
6. His infinite auspicious qualities – in number, extent etc. and being without any limitation of any kind.
7. His reciting the Vedas constantly in the form of Hayagriva.
8. His face with the radiance of thousand moons which will remove the misery of the world just by contemplation.
9. His totally effortless control over the world – indicated by the twitching of His eye brows being adequate to confer even the positions of the Creator of the world etc.
10. The necessity to think of Him always, specially when one anticipates his end. This gives the indication that the last thoughts of a dying person, which can only be determined by his priorites in life, will have decisive effect on his future lives. 
11. The epithets used for addressing God are also most appropriate – Sreepathi – who is worshipped by all other gods, Isha – who is the lord of Lakshmi herself, the mother of all others, Vishnu – being sarvavyapi and Anantha, Hari – who destroys the causes of our misery and suffering (evil), Vaikunta – who always recites the Vedas, thus giving continuity to them even at the time of universal dissolution, Govinda – the main diety extolled by the Vedas, Raama – the one form which gave pleasure even to the onlookers when they saw Him and who will remove the sorrow and the pain of the world, Anantha – who is infinte in space, time and qualities and whose extent no one but Himself knows – as it is said that Lakshmi, His eternal consort who has been with Him with no break since beginningless time is yet to complete her understanding of the extent of His qualities with respect to a nail of His.
Further thinking about the words, phrases used, appellations for God, directions for action (Vidhi Vakya) etc will perhaps give far more understanding. Thus Dvadasha Sthothra flowing from the devotion filled mind of the Sarvajna who founded the Thathvavada philosophy is inspired, mystical, accurate, and most efficacious in giving the desired results for those who recite it with understanding and devotion.