A monocle is most likely to be any of the many monocles created by Dusk Gleam, who usually wears one on her left eye. She is quite upset if one is damaged, but she has many so they are entirely replaceable.
Dusk's currently worn monocle ascends with her when she's in Nightfire Mode, but exactly how this affects the device, if at all, is unknown.
Jake Smith possesses one monocle Dusk gave him to protect him from subterfuge, although he has neglected to actually use it and she has fooled him herself at least once.
The frame of the monocle - that is, the yellow round part on the bottom and the black part around the lens - is essentially a small computer. Like all of Dusk's machinery, it synchronizes to her main database whenever possible and allows her to access information and display it within the lens.
The lens is not only usable as a display screen, but if Dusk presses upon the yellow bulb part and swings the monocle, the frame opens and the lens will fly out like a disc. Individual lenses will be either blunted or sharpened depending on whether she expects to have to cut anyone with it - she usually has it blunted to avoid tragic accidents.
The monocle can detect certain information about an individual, including their address, meaning that Dusk is capable of identifying individuals regardless of their physical condition, if she is familiar with the address.
And as stated above, the lens can be launched like a disc as an impromptu projectile weapon. This will disable the monocle until a new lens is fitted. Flicking and aiming this properly takes practice.