What does the term 'divers places' mean?
Divers is an archaic spelling of diverse, meaning many and varied places, or a lot of different places.
Source.
EDIT: A better source confirms here.
The word divers is an old spelling of diverse. The phrase divers places just means "many different places".
As the other answers have noted, divers can be seen as an archaic spelling for the modern word diverse. However, the OED gives four senses for divers (my paraphrasing):
Different in kind.† Corresponds to the modern use of diversity, as in gender diversity or diversity jurisdiction.
Evil or adverse.† Obsolete since the 1600s.
Various or several. Described in the OED as "somewhat archaic, but well known in legal and scriptural phraseology."
As an adverb.† Obsolete, and not semantically distinct from the other three senses.
The alternative Bible translations linked in the comments confirm that here, divers places means various places (sense 3). However, the OED also provides a Biblical citation for sense 1:
And they gave them drink in vessels of gold, (the vessels being diverse one from another,) and royal wine in abundance, according to the state of the king (Esther 1:7, KJV).
As to the legal variant of sense 3, the phrases divers other places, divers other persons and divers other times were traditionally used in English criminal indictments. For example:
That T.B. ... together with divers other evil disposed persons, to the number of one thousand and more, whose names are to the jurors aforesaid as yet unknown ... did then and there and on divers other days and times, as well before as afterwards, in a violent and tumultuous manner meet and assemble together, at, &c. aforesaid, and divers other places ...
These phrases continue to be used in some common law jurisdictions, such as the Australian state of Victoria (at least as late as 2012). For example, in Dickson v The Queen [2010] HCA 30:
The particulars of the offence stated that at Melbourne and divers other places in Victoria between 22 December 2003 and 20 January 2004 the appellant had conspired with three named persons ... and that they had agreed to pursue a course of conduct which would involve the commission by them of an offence ... [3].
† The dagger is used in the OED to mark obsolescence.