EMILY: Your father is now the president and CEO of the Gilmore Group, an international insurance consulting firm.
LORELAI: Wow, that’s great. So, um, what’s the . . . like, how does . . . what’s his job? …
EMILY: Your father is an international insurance consultant … He consults on matters relating to international insurance.
Lorelai has no idea what an insurance consultant does, Emily doesn’t really know, and I’m not sure the writer (Allan Heinberg) knows either! I’m a bit in the dark too, because they usually work for an insurance company, and are basically sales agents. I presume an independent insurance consultant would help businesses choose from various insurance plan options, and sell insurance policies from a range of insurance carriers, rather than one. Don’t ask me how a single person can be a “group”.