What’s wrong with my treadmill and how can I fix it?

As it is now, it is dangerous to use. Unplug it and don't use it again until you have it repaired and inspected. If you try to use it, it could start a fire.

A sensor has detected overheating. This might be the result of too much current in a circuit, or the result of a mechanical problem. It could be both. 

When the tripped sensor cools, it is possible to restart the treadmill.  But, repeated tripping indicates a serious problem. If you force it to restart, you could be making the problem worse, causing additional damage, and increasing the risk of causing a fire.

The popping and burning smell indicate additional damage has occurred, and there is significant risk of fire. 

Some possibilities:

* The motor is working too hard. One cause of this is suggested by a previous answer: The treadmill needs lubrication. The belt / bed might need lubrication. The motor, bearings, and other moving interior parts may need lubrication.

* The motor is not receiving enough cooling air. Vents may be clogged with dust. Fans may be dusty.

* The belt might have been adjusted with too much tension.

* Some other electrical component may have failed, or be close to failing.

* An electrical connection is failing.

If the damage is repaired, the components cleaned, and it passes inspection, consult your owner's manual for proper lubrication. You could cause problems by using the wrong type of lubricant.

Comment: My father had a treadmill that was self lubricating. Lubricant was built into the bed, and would be released as the bed wore down. 

Sounds like it needs lubrication.  When was it last oiled?  It is possible that some need more oil than others.