Bricking
"Bricking" is a term that refers to a botched "jailbreak," "root" or modification. Basically, when your device's system crashes during an attempt to change the firmware outside of manufacturer allowed means, it's been "bricked" ̵2; turned into a "brick" with no functionality whatsoever.
Newer Model
Your PSP may have been bricked while using Hellcat's Recovery Flasher simply because you're using too new a model. PSP3000 models are notorious for bricking while attempting to use the recovery flasher, while older models like the PSP2000 are considerably more stable.
Incompatible Firmware and IPL
According to the Hellcat Recovery Flasher read-me file, if the Initial Program Load and the firmware image being flashed to the PSP aren't compatible, the system will become bricked without fail. Making sure the IPL and firmware package match is key to preserving your system.
Missing or Damaged Files during Restoration
If you're restoring a previous firmware package in its entirety but some of the necessary files for the new firmware package are missing or even simply damage or corrupted, you run the risk of bricking your PSP. Without certain key files available for the firmware's functions, there's no telling what might happen during operation. Glitches, bugs and other problems are likely, but a bricking is the worst-case scenario. Depending on the extent of the damage or which files aren't available, the likelihood of bricking can increase or decrease.
Caution
Before you attempt to add custom firmware to your PSP, understand that any modification of this kind runs the risk of bricking the system. Sometimes a bricked system can be restored; sometimes it can't. If you aren't willing to risk the money you invested in the system, don't attempt to install custom firmware. Also, changing the firmware on your PSP is against Sony policy and will void your warranty. Modify your PSP at your own risk.