As opposed to negative feedback.
Positive feedback occurs if something causes itself to become more/stronger over time. An example of this is money in a bank account, which accumulates interest. So the more money you have, the more money you get.
Positive feedback also means that negative values will become more negative over time. To use the example of banks again, this would be like a loan, where you owe the bank more and more money over time, again due to interest.
So a system with positive feedback will tend towards extremes. An existing condition is reinforced. That means that if you put € 10 into a bank account, you will be rich in a few hundred years. But even if you only owe the bank € 10, you will be hopelessly indebted in a few hundred years.
Examples (10% positive feedback per time unit):
time value 1 value 2
0 10 -10
1 11 -11
2 12.1 -12.1
3 13.31 -13.31
100 137806 -137806
t=inf. +inf. -inf.
Value 1, which is already positive, becomes greater over time, while value 2 becomes more negative because it is already negative to start with.
Positive feedback is often called "explosive", because all explosions are caused by positive feedback. When a chemical explosive is heated sufficiently, some of its molecules will combust, increasing the temperature of the substance, which causes many more molecules to combust:
If the combustion of one molecule releases enough heat to combust ten more molecules, then one single molecule combustion will result in ten, which will result in a hundred, which will result in a thousand, which will result in ten thousand combustions, and so on. Boom.
Positive feedback is usually destructive, so it has little use apart from destruction. One notable exception is money. Money can be invested to make more money. And since you can never have too much money, that is a good thing. Economic systems depend on this effect to function.
Most of the time, though, positive feedback is annoying, or even dangerous. The squealing caused by holding a microphone too close to its own loudspeakers is an example of the "annoying" category. Stock market crashes are a case of dangerous positive feedback, as are nuclear explosions.