A private credit firm is a non-bank entity that raises money from wealthy investors, pension funds, etc to loan out to businesses. The funds are generally locked up for several years to match the duration of the loans.

They also borrow money from banks to add leverage to this basic setup.

Not who you asked, but I think making the nuance between retail and corporate credit. With firms being corporate credit (i.e. we aren’t talking about individuals / retail).

> What is the definition/significance of "firm"

Broadly speaking, privately-held companies are called firms. Colloquially, it tends to connote closely-held companies.