Why did the cord on my charger turn yellow and part of the white cord covering is exposed showing copper?

The cord material can deteriorate due to sunlight, excessive heat, or excessive stress, or all of those. If you wind the cord around the "ears" be sure to make a 1 to 2 -in loop in the air first, before you start to wind against the "ears" to provide some randomization and move the initial contact point slightly each time it is re-wound.

If there is a short circuit in the MagSafe end, it can make that part extra hot, (there is a tiny circuit board in there) which adds additional stress.

Exposed and showing copper COULD be seen as a safety issue, although the voltages involved are 16 Volts DC or less. You should ask at the Genius Bar of an Apple-owned store, if available in your area of the world. The worst they can say is NO. A new one if you have to pay is about US$80.

Be sure to make an appointment or you may have to wait half a day or more. Your appointment for an evaluation and over-the-counter diagnostic is free, in warranty or out. Be sure to bring all pertinent equipment, (e.g., not just the power adapter or not just the computer)