In the United States, a conforming loan is a mortgage loan that conforms to GSE (Fannie Mae and Freddie Mac) guidelines. The most well-known guideline is the size of the loan, which, for 2019, was generally limited to $484,350 for single family homes in the continental US. Other guidelines include borrower's loan-to-value ratio (i.e. the size of down payment), debt-to-income ratio, credit score and history, documentation requirements, etc.
In general, any loan that does not meet guidelines is a non-conforming loan. A loan that does not meet guidelines specifically because the loan amount exceeds the guideline limits is known as a jumbo loan.