firmware is the software version its running it will normally say 1.02 or similar.
It should show this when you boot it up. I suspect theyre asking because some updates of firmware or flashes cannot be reversed and wont allow them to play pirated stuff. hope that helps
To see which version of PSP firmware you are running on your PSP, clickthe "Home" button. This will get you to the top level navigation where you can move between functions. Use the left arrow to move all the way to "Settings", then scroll to "System Settings".
Click "X" to select "System Settings" and you'll see "System Information".
Click the "X" button again and you'll see version of the firmware you have on your PSP.
If it's a later version it will show 2.60 etc. If it's an early one and still on version 1.02 etc DON'T update it, it's worth more to the hackers as previously stated.
With the use of a 'PSP Pandora Battery' and a 'magic memory stick' (both very easy to aquire / make yourself) any official Sony PSP Firmware is currently downgradable to the more useful exploitable firmwares.
There are some newer PSPs out that have physically been altered by Sony to prevent the downgrade hack from working on them but as far as I know those PSPs are currently only available in Asia, plus I don't think it'll take the PSP God Dark_Alex long to crack them
Be aware if you post ANYTHING on ebay publically regarding cracked/patches/modded/etc games consoles you risk your item being removed and banned in some extreme cases.