1
general::
Many; also, no particular amount of. The meaning here depends on the context. I can give you any number of reasons for John's absence means I can offer many reasons. Any number of subscribers might stay home means that an unknown number will not attend.
American Heritage Idioms
2
general::
Phrase(s): any number of someone or something
Fig. a large number; a sufficiently large number. (Used when the exact number is not important.) • Any number of people can vouch for my honesty. • I can give you any number of reasons why I should join the army. • I ate at that diner any number of times and never became ill.
McGrawhill's American Idioms And Phrasal Verbs