What does it mean when a dog cannot open one eye?

The inability to open one eye could indicate a number of conditions, including injury to the eye, infection, allergic reaction, foreign objects in the eyeball or under the eyelid, or hypersensitivity to light. These are just a few possibilities. Ophthalmological issues can quickly turn serious and even small injures can cause blindness if left unattended, so I would see a veterinarian immediately to determine the actual cause.