It's never good to operate an engine with coolant issues. There are many things that could be wrong.
Lets start with the basics.
Your car uses the coolant to keep the engine at operating temperature, in other words to reject waste heat. To do this, a coolant pump, driven by the engine circulates coolant through the engine and to a radiator so that heat can pass to the surrounding air. When the vehicle is sitting or moving slow, there is not much air to take that heat away, so there is an electric fan to help with the air flow.
The coolant pump has bearings to let it rotate freely, and a seal to keep coolant from destroying the bearings.
If the coolant pump seal fails, the coolant that gets past it will drain out of a hole before the bearings and drain to the ground. At this point the coolant pump failure is not far away. Once the bearings are exposed to coolant that will get noisy. At first a grumbling, then a squeal, and finally mechanical failure, which may destroy the engine.
When an engine has coolant leakage issues, usually air gets into the cooling system and, of course, rises to the top of the engine, preventing any coolant from getting to the hottest parts of the engine, which is the cylinder head. When this happens, there is no coolant for the fan switch to sense, and even though the engine desperately needs to be cooled, the fan doesn't come on and things get hotter and hotter.
You may have multiple problems now, since the engine has almost certainly overheated.
Water pump failed.
Air in coolant system.
Cylinder head has warped and there is no seal between two or more cylinders.
This is not a do it yourself fix. Take it to a shop and have it diagnosed. You might be really, really lucky and only have the water pump issue, but don't get your hopes up. Do not drive the car or start the engine.
Sorry for the alarming news.