THX Certified means that they meet the THX quality standard for [in the case of speakers/decoders] sound reproduction specified in the THX standard. The standard, and associated certification program are defined and administered by THX Ltd (a spin-off from LucasArts)

So the literal answer to your question is: Logitech made an application to THX for certification; THX tested some amount of Z-5500s using their own test environment, equipment and test programmes; THX found that the speakers are sufficiently high quality to certify; THX approve the certification and permit Logitech to use the THX logo in the manual, packaging, and marketing material for that model of speaker.

These really are excellent speakers -- I've had mine for about 15 months, and the difference in quality compared to my old 5.1 system is amazing.

Z-5500 specific: Be warned: the subwoofer is NOT magnetically shielded, so the system comes with a warning not to put electrical devices (PCs, mobile phones, etc) within two feet of it. That said, mine hasn't yet destroyed or damaged anything nearby. Also, apparently there's a fault in the power circuit design. Unplugging and.or turning it off at the sub can easily blow the fuse. This only happened to me once, but then I've only ever unplugged it once. My tip: set it up, plug it in, never turn it off -- standby power consumption is negligible. If you do blow the sub's fuse, contact Logitech and they'll send you some more.