Now how does this exactly happen?

When a lot of traders expect a price to decrease, because they think the stock is overvalued, they start to short that stock. 

When the sellers take the upper hand, the stock price will decrease. However, when a stock is shorted and the price does not decrease but increases, because of some good news for example, traders that are short may close their positions to avoid losses or bigger losses. Or worse, their brokers might close the position for them because of a margin call.

Now, when a stock is very heavily shorted and, unlike expectations, the stock price rises significantly, a lot of traders might simultaneously start closing their short positions. Closing a short position is done by buying the shares back from the market, so that you can return them to your broker. And when they all start buying those shares, they all push the price even higher.

At a certain moment, the stock price starts increasing so fast, that most traders that are short, are forced to close their positions. At that moment, the price shoots up drastically, and the short squeeze is a fact.

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Rare event because of opposing conditions

Short squeezes are rather rare because two opposing conditions must be fulfilled: on the one hand, a stock should be shorted really heavily because traders think the price will decrease and on the other hand, an external factor, such as good news, should be pushing the price higher. 

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