"Persons" is only really used in formal written English. Even then, it is usually best avoided. Here's an example of the sort of document where you'd expect to find it in use: http://www.nelsoncountyserviceauthority.com/images/meetingcodeofbehavior.pdf

"Persons" => old-fashioned plural of person :)

DOES the word "persons" exist in English? Technically yes, but only in the context of "individuals". The regular plural of "person" is "people", and it's very rare for a native speaker to use "persons". Using "persons" as the general plural of "person" is a common learner mistake. Try to avoid it.

"person" is one individual, and "persons" is the plural form. "people" is for a group of persons and "peoples" is the plural form. "people" is used in everyday speech for "persons" and "peoples", with those two words being quite formal.