We have all seen signs saying "All Major Credit Cards Accepted". What is a minor credit card?

There's no cards specicially labelled "minor" credit cards. The "major" designation is used for brand names like Visa, MasterCard, Amex and Discover that are accepted in the majority of locations. (In the case of the U.S) Most credit cards are local cards or a smaller national chain cards, such as a department chain card (Sears, JC Penney) or a gas card.

http://www.creditcardguide.com/creditcards/credit-cards-general/major-credit-card-companies/

http://www.creditcardguide.com/creditcards/credit-cards-general/guide-types-credit-cards/