ApannArti-prashamana-vidhau baddha-dIkShasya viShNoH
        AcakhyustvAM priya-sahacarIm aikamatyopapannAM
    prAdurbhAvairapi sama-tanuH prAdhvam anvIyase tvaM
        dUrotkShiptairiva madhuratA dugdharAshestara~NgaiH

Lord Vishnu has vowed to (dedicated Himself to) always engage in the act
of curing the distress has afflicted people; The Vedas proclaim that in this
divine act, You are completely in agreement with His wishes, and lovingly
accompany Him in everything; Just like waves from the Milky Ocean when they
are spread far and wide still bring sweetness with the waves, You make
matching Avatars (like Sita for Rama and Radha for Krishna) with the Lord and 
accompany Him most suitably.
==
Apanna = afflicted by, fallen into
Arti = distress
prashamana = curing, healing
vidhau = in the act
baddha-dIkShasya = of One who has dedicated/committed oneself to do something,
                   especially a Vratam or sacrifice
viShNoH = of Lord Vishnu
tvAm = You (sujective form)
aika-matya = unanimity, agreement of opinion
upapannAm = accompanied by, in company with 
priya = beloved
sahacarIm = One who accompanies in doing everything
AcakhyuH = (the Vedas) declare as
dUra = far
utkShiptaiH = by somethings thrown 
dugdha-rAsheH = of the Milky Ocean
tara~NgaiH = with the waves
madhuratA iva = like sweetness, sugar 
tvam = You
prAdurbhAvaiH api = by the incarnations/Avataras also
sama-tanuH = equally matching, well proportioned body
prAdhvam = favourably, comfortably, suitably (avyayaH)
anvIyase = follow, accompany
==
[pad, 4 A, padyate, to go to, approach; attain, obtain; Apadyate = to fall into
 misfortune; Apad, ApattiH = calamity]
[sham, 4 P, shAmyati, to appease, calm down; to cease, put an end to;
 prashAmyati = to terminate; quench; subdue; prashAnta = calmed; sedate]
[bandh, 9 P, badhnAti, to bind, tie; to form, arrange; produce]
[dIkSh, 1 A, dIkShate, to consecrate, prepare oneself for a sacred act]
[man, 4, 8 A, manyatE, manutE, to think, imagine, conceive; matiH = intellect; 
 matam = opinion]
[khyA, 2 P, khyAti, to tell, declare; to be named; AkhyAti = declare, announce, 
 narrate; AcakhyuH - kartari-liT-prathama-puruSha-bahuvacanam]
[kShip, 6 U, kShipati/te, to throw, cast, dispath; utkShipati = tossed, raised]
[duh, 2 U, dOgdhi, to milk; squeeze out; to drain; to grant a desire]
[i, 2 P, eti, to go towards; arrive at, obtain; arise; anveti = accompany; 
 follow, succeed; anvIyase - karmaNi-laT-madhyama-puruSha-ekavacanam]