A short squeeze happens when almost all of the trading volume is shorts capitulating (buying) at the same time new shorts are establishing new positions (selling).
When the buyers are covering their short position and the sellers are less sophisticated short sellers establishing new positions, the price can rise while the short interest stays very high. Usually this happens when the smart money is also buying and covering a short position becomes increasingly difficult. Buy stop orders are triggered causing short sellers to drive the price higher as they try to limit their losses. Because the buyers/owners strongly believe in the integrity of the management, they are not willing to sell. As the price of the stock vaults higher, the only way for the shorts to limit their losses is to buy at the market which drives the price even higher. It becomes a frenzy!