In a normal co-location (colo for short) a provider has a data hall, where they install servers of various kinds for their customers. The colo stands for power and connectivity, and some level of out-of-band monitoring to do billing or capping.
The monitoring is usually on the network level, from switches and packet flows, and not internal to your server ("what is running now") and is used to prevent customers from interfering with others, and to alert customers in case of their servers failing.