An archive is a group of documents that was brought together in antiquity for a specific reason. Archives can be concerned with either public or family matters. An archive may have been discovered together, preserved from antiquity in a single location that was unearthed by archaeologists, or it may be the result of scholarly reconstruction of links between ancient documents.
In the case of the Zenon papyri, all of the documents associated with the archive were discovered together, in the same location in the ancient town of Philadelphia. The Zenon archive all belonged to a single individual, Zenon, and represent the documents that he believed were important enough to keep and collect together.
A similar discovery of a group of documents was made at the site of Karanis. Here you can see a photograph taken in 1930, when a group of documents was discovered beneath the doorsill of a house at the site. We do not know the exact circumstances of the discovery of the Zenon archive at Philadelphia, but it seems likely that all of the papyri originally collected by Zenon were found together.
For more information about papyrus archives, you can visit the Leuven Homepage of Archives and Collections.