Meaning

• exhaust someone’s energies or resources by leading a hectic life
• to engage in an activity, usually work-related, from early morning until late at night
• to work so hard that you don’t rest
• to spend all of your energy on two pursuits at the same time

This is my understanding:

So when you burn the candle at both ends it means you’re working really, really hard and you’re working really, really fast. I’ve been burning the candle at both ends lately so I’m pretty tired and this is the last thing I need to do today. But I had a day full of all kinds of different jobs and I worked really hard, and I worked really fast. You know what a candle is right? It’s a tall wax thing with a wick in the middle and you light the top and it has a small flame. But if you lay a candle sideways you can light both ends and the candle is twice as bright, but it burns out twice as quickly. People are the same if you burn the candle at both ends at your job you’re probably going to get tired a lot more quickly and you’re probably going to eventually burn out a little bit. So, burning the candle at both ends means working really, really hard.

I said my “two cents”. Let me hear your interpretation in the comments.