I'm sure it's a test strip printer. I've seen something similar in function which had numbers that also printed in the margin to let you know which strip was which.
To use it you would think up a series of exposures you want to test.
Put a piece of paper in and place it where the easel will go for the final print.
Expose for a test time, say 10 seconds. Push the button to advance to the next step.
Expose for another test time, say 20 seconds. Push the button to advance.
Expose maybe for 40 seconds this time. Push the button.
After you develop the little print, you'll see what step looked good and you can remember what time you used for that step.... and then use it for the final print.
(Of course nothing's ever final when it comes to printing... but that's how you would use this device).