Your cars engine oil is an important lubricant in your engine. It allows metal press against each other without causing any damage in your engine. The oil lubricates the pistons as they move up and down in the cylinders and without any oil inside your engine, the metal against metal will cause friction and will create so much heat that metal could weld together damaging the engine.
If you have oil in the engine but never change it then dirt can build up within the oil. Of course the oil filter removes dirt but sooner or later the filter will not be able to hold anymore dirt and it will get in to the engine oil causing the engine components to wear faster.
Eventually, as the engine oil builds up enough dirt, it will stop lubricating and the engine will fail. This won’t happen if you neglect to change your oil when it was past due for a month, I wouldn’t want you to panic if it has be about that long since you last had an oil change. It would take a couple thousands of miles running on the same engine oil through the engine for a long time to cause any serious damage but if you want your engine to always be running in tip top condition and last for a very long time, then you should change your engine oil when it is due.