This is just one of a lot of such sayings or beliefs.The following (modified) sentence appears in 'Macbeth' ..."By the tingling of my thumbs, something wicked this way comes." (It's not 'tingling' in Shakespeare's version, but I'm sure AnswerBank won't allow me to use the actual word. If you need a clue, it's what you feel if you stick a needle into your finger.)
There's also the idea, if you shiver, that that means someone is walking over your eventual grave-site. An itchy palm means money is coming your way and there are many other similar beliefs.
All of these examples are superstitious hangovers from the days of witchcraft/angels etc, when people believed they were constantly being offered signs and warnings of distant or future events.
The idea that 'burning' ears means someone somewhere is talking about you is just another illustration of the same idea. The notion presumably is that you are desperately anxious to hear what they're actually saying. The grave one suggests the feeling of horror at the desecration of a grave...especially your own!