Conforming loans are a type of Conventional loan that fit the mortgage criteria established by Fannie Mae and Freddie Mac. Fannie Mae and Freddie Mac are "government sponsored entities" (GSE) that behaves like a corporation but is created by the US Government/Congress.
Fannie and Freddie set guidelines on the yearly conforming loan limit and the underwriting criteria (eg. max Loan to Value ratio, max Debt to Income ratio, min Credit score, etc.). Loans that do not meet the guidelines are considered non-conforming.