What is the meaning behind the title "Provenance" of Person of Interest S03E14?
A simple Google search will tell you Provenance is:
the place of origin or earliest known history of something.
A more detailed Wikipedia listing describes it as:
Provenance (from the French provenir, "to come from"), is the chronology of the ownership, custody or location of a historical object. The term was originally mostly used in relation to works of art, but is now used in similar senses in a wide range of fields, including archaeology, paleontology, archives, manuscripts, printed books, and science and computing. The primary purpose of tracing the provenance of an object or entity is normally to provide contextual and circumstantial evidence for its original production or discovery, by establishing, as far as practicable, its later history, especially the sequences of its formal ownership, custody, and places of storage. The practice has a particular value in helping authenticate objects. Comparative techniques, expert opinions, and the results of scientific tests may also be used to these ends, but establishing provenance is essentially a matter of documentation.
I've italicized that particular section to indicate how it relates to demonstrating the authenticity of an object - something particular important when dealing with thievery (as this episode does).
From the same Wikipedia page:
The provenance of works of fine art, antiques and antiquities is of great importance, especially to their owner. There are a number of reasons why painting provenance is important, which mostly also apply to other types of fine art. A good provenance increases the value of a painting, and establishing provenance may help confirm the date, artist and, especially for portraits, the subject of a painting. It may confirm whether a painting is genuinely of the period it seems to date from. The provenance of paintings can help resolve ownership disputes.
So given this episode is an antiquities heist, the word Provenance is being used to both relate to the fact the episode is dealing with art and to highlight the important of ascertaining the authenticity of said art (since doing so will greatly increase its price - again, vital to know for any robbery!)