Imagine a physical burn's pain to grasp how someone feels after a bad decision. He decided to quit his job impulsively and really burnt his fingers.
Pro Tip 2/3
Practical Caution
Use it to advise caution based on past mistakes without specifying the details. Remember when you burnt your fingers last time? Think twice before acting.
Pro Tip 3/3
Severity Implied
The phrase suggests the consequences were serious enough to teach a memorable lesson. She really burnt her fingers with that investment – I doubt she'll speculate again.