Ah, okay, I get it.
What they did is they enabled encryption for their wireless router. Doing so does add a bit of security to your wireless network, but anyone with the right knowledge or applications can easily bypass it. The most common two encryption methods used are the more secure Wi-Fi Protected Access (WPA), and the older Wireless Equivalent Privacy (WEP).
If you have a Nintendo DS or Nintendo DS Lite and wish for them to be able to access your network, WEP is recommended. Otherwise, WPA would be better. I have no idea what the PSP supports, so you may want to look into that at Sony's support page. =)
As to how to go about setting it up, that depends on your router's manufacturer, since every company supplies a different means of modifying router settings. Usually, it is done through the browser, though sometimes it is done via an application. The setting will likely be called something like "WAN security", or passwords, or something similar. Again, this all depends on the manufacturer and model of the router.
If you need more clear instructions, then I'd check out the router's instruction manuel. You can usually find them on the manufacturer's support website. If you need help with an Apple, Buffalo, or a Netgear (the most difficult, alongside ]Uh.. Okay. I think I get it. Thanks I'll try it now.