Blue smoke means oil is getting into the combustion chamber; usually mean worn out piston rings.
Normally smoking is caused by piston rings wearing out, it needs an oil change, or is overfilled and sucking oil into the carb.
I am assuming that the mower doesn't start.... My first guess would be that you are not getting spark to ignite the gas in the engine. Check to see if you have spark at the spark plug.
If it is a push mower there are only a couple things that will cause the mower to smoke. 1) The rings are worn and need replaced. This lets oil seep past the rings and burns the oil in the cylinder. This will cause a white smoke. (this is probably the most common cause for engines smoking) 2) The carburetor is putting too much gas in the engine. This will cause the engine to run rich and make a black smoke. 3) There is an external oil or gas leak that is leaking onto the motor and burning from the heat of the engine. If it is a riding mower there are many more things that could cause it to smoke.
It is need of a service.
One reason that a lawn mower may begin to smoke is that the oil chamber is too full. Spark plugs that have burnt oil and are not cleaned can create smoke and other exhaust issues.
its burning oil :(
Some engine oil has entered the muffler when the mower was tipped, it will burn off after you run it, make sure the oil level is correct (don't overfill) as this can cause similar problems.
Oil burning
bad smoke
If all oil the mower will not start. If only a little oil, the mower may start but run rough and smoke very much.
its probably burning oil, if the smoke is white. if the smoke is black, it means its running rich. if the smoke is white, you have serious internal engine problems
When you overfill oil in a lawnmower it will smoke when you tip it sideways while mowing,it has no harm