atho muhūrta ekasmin
nānāgāreṣu tāḥ striyaḥ
yathopayeme bhagavān
tāvad-rūpa-dharo 'vyayaḥ
atha u -- and then; muhurte -- at the auspicious time; ekasmin -- same; nana -- various; agareshu -- in residences; tah -- those; striyah -- women; yatha -- properly; upayeme -- married; bhagavan -- the Supreme Lord; tavat -- that many; rupa -- forms; dharah -- assuming; avyayah -- the imperishable one.
As Srila Sridhara Svami explains, here the word yatha indicates that each marriage was duly performed. This means that the entire company of the Lords relatives, including His mother Devaki, appeared in each and every palace and attended each and every wedding. Since all these weddings took place simultaneously, this event was surely a manifestation of the Lords inconceivable potency.
When Lord Krishna does things, He does them in style. So it is not astonishing that the Lord simultaneously appeared in 16,100 wedding ceremonies taking place in 16,100 royal palaces, accompanied in each palace by all His relatives. Indeed, this is the way one would expect the Supreme Personality of Godhead to do things. After all, He is not an ordinary human being.
Srila Sridhara Svami further explains that on this particular occasion the Lord manifested His original form in each of His palaces. In other words, to take part in the wedding vows, He manifested identical forms (prakasa) in all the palaces.