Grey colored smoke from a vehicles exhaust system means that your vehicle is burning oil.
The engine could be burning oil due to worn valve seals, bad piston rings, worn cylinder walls etc.
An engine burning oil and smoking will not usually cause any harm to the engine but it's best to have it checked out and fixed if possible.
I have driven an old car that was putting out grey colored smoke and burning oil for around 100,000 miles and 10 years before the car gave up due to a bad transmission.
The engine was still running.
The old car was just an old beater car that I used to get to work and back and was not worth paying to have fixed.
But if your car is worth it then it's best to have it fixed.
Just also make sure to check your engine oil often as well.