What does it mean if half my big toenail is blue-gray in colour? its not due to trauma..

Nail: Don't dismiss this. Nail changes as you describe are often from shoe pressure and it is often from shoes with low toe box. The nails can have skin lesions like a mole as well. These are most often benign but should have a trained eye look at them. Just to make sure...See your doc.

Shoe pressure?: Could be a sub ungul hematoma caused by shoe style.