Could someone please tell me what it does, or at least what it's called, so I can look it up?
Scottbb's answer is correct and you should accept it, but I wanted to follow up with a little more information about how to find the answer in case you have others like it.
There's a diagram on page 6 of the Nikon D5500 user manual (PDF) that describes the different parts of the viewfinder display, including this detail:
This is a detail that shows every segment of the display all at once, so I can see how you might not immediately notice that it includes the
[r 2] part that you're asking about. But if you look in the place in this detail where the
[r 2] message appears in your camera, you'll see
[88.8] called out as item 13, and that item is described in the text below:
Number of exposures remaining.......................................31
Number of shots remaining before memory buffer fills.............37
White balance recording indicator Exposure compensation value....72
Flash compensation value ..........12
Capture mode indicator
So this part of the display actually serves six different purposes. They're not described in all that much detail on their respective pages, but I think it's enough. Page 31 again shows the corresponding part of the rear display (which also uses the bracket notation) and calls it "number of exposures remaining," including the helpful detail that a K is displayed as a 1000's multiplier if you have more than 1000 exposures left. Page 37 shows the viewfinder display that you see when you half-press the shutter release button, and labels the bracket area (this time including the 'r') as "buffer capacity."
The D5500 reference manual (PDF) contains similar diagrams with page references, and has a more detailed description of the buffer size indicator on page 73:
Buffer Size: The approximate number of images that can be stored in the memory buffer at current settings is shown in the viewfinder
exposure-count display while the shutter-release button is pressed.
So the information you need is in the manual, it's just a little hard to recognize in that initial diagram.