I think that what happened in the evolution of the real world was that the earliest mammal (still during the age of dinosaurs) was nocturnal (perhaps to avoid being eaten).
Being nocturnal, they lost the ability to see in color ... or they traded it for the ability to see in low-light conditions.
See Rods & Cones:
Rods are responsible for vision at low light levels (scotopic vision). They do not mediate color vision, and have a low spatial acuity.
Cones are active at higher light levels (photopic vision), are capable of color vision and are responsible for high spatial acuity.
After the end of the age of dinosaurs (about 65 million years ago) mammals evolved to become more dominant, no longer only nocturnal (but most mammal species retained monochromatic eyesight, since there was no especially compelling reason to evolve or select for color vision).
Plants were evolving too: by that time they had flowers, and maybe fruit. The theory is that fruit would become red to indicate when it was ripe (ready to be eaten), which (being red) was a signal that could be seen by birds (birds, not being mammals, never lost their original color vision).
At this point in history, primates (i.e. climbing monkeys), alone of all the mammals, re-aquired (evolved) ability to see in color again -- this would help them see ripe fruit (i.e. join the communication that was already happening between the fruiting plants and the birds). Humans, being primates, also have this color vision.
So, humans with monochromatic eyes: perhaps there wasn't colored fruit to see; maybe there was fruit but fruit didn't bother to change color when ripe (e.g. because birds didn't see in color).
Some possible results:
- Maybe humans wouldn't be keen on sweet/sugar.
- Maybe they'd be nocturnal, see better in the dark; and if it's true that mammals evolved warm-bloodedness and fur to be able move about at night even when it's cold, maybe nocturnal monochromatic humans would also still be furry.
- Maybe humans couldn't see fine detail (if cones are responsible for "high spatial acuity" as well as a color) ... which might wipe out a lot of technology, i.e. everything from weaving cloth to vascular surgery, not to mention reading and soldering etc.
- Maybe humans would have some other sense instead: better sense of hearing or touch, splendid sense of smell, or greater intelligence (intelligence is complex and can be measured along many axes, but maybe for example they'd be less careless, better at paying attention before they act).
- Maybe they'd prefer low-light conditions: e.g. caves or deep forest.