The centers of your eyes see in high definition, but the larger receptive fields in the periphery see in low-def, creating the illusion of a discolored dot at the grid intersections.
If you try to focus on the black dots, they will disappear because you are seeing them only in your peripheral vision.1,2
1 Anstis S. Picturing peripheral acuity. Perception. 1998;817-825.
2 Spillman L. From elements to perception: local and global processing in visual neurons. Perception. 1999;28:1481-1492.