The sixth line in our image caption example reads "70.1208." This is Soir Bleu's accession number, as assigned by The Whitney Museum of American Art.
An accession number is internal to the institution, and is given by curatorial staff to every object that is taken into legal possession. Each accession number is unique, may contain both letters and numbers, and comes in two or three segments separated by decimal points. What you won't see are whole words spelled out because these numbers are, at their most basic level, a form of inventory and thus need to be kept short and sweet.
As with other things like object dimensions and donors, an accession number isn't something you'll come across in an art history exam. You are completely free to disregard it, now that you know why it's there and what it stands for. It is simply present, when it is present, at the request of the museum which has granted permission to reproduce an image - as long as thus-and-so is included in the captioning.
