Hi mobile world I met many times the term "host controller" or "baseband controller" used interchangeably in the context of being the heart of the mobile. What exaclty is that, som SoC with CPU, GPU, GSM modem???
Typically the 'host' refers to the master device/entity that belongs to the side of the computer. It could be inside computer or external to a computer. [it could be a microcontroller , but the point is host is more closer to you when you writing software to work with].
The main idea is before you communicate with the other device, you communicate with the host, for a example hard disk controller is a host, USB controller chip is a host.
So according to your GSM module thing, The chip hardware/software that parsing the AT command set and act as a front end is refereed as a host.
Your Manual/Specification probably should have a chapter called terms and Abbreviations. Turn out for that page and you'll find the specific abbreviation which is specific to your module.