The hardware sits in the organization's own data center or a facility it controls, so data does not leave the premises. It is common in regulated sectors such as healthcare, finance and government, and where data must stay within a country or a secure network, sometimes without any internet connection.
It gives the most control, but also the most work: buying and powering GPUs, cooling them, keeping software current and planning capacity. Hardware has a long lead time and ages quickly as new chips arrive.
Staff skills matter too. Running large models well takes people who understand both infrastructure and machine learning.
Estimate demand before you buy, plan for power and cooling, set up patching and monitoring as for any critical server and keep a fallback for when the hardware is down.