A formal concept is an idea or category defined by a concrete or specific set of rules, guidelines, or properties. For a concept to be considered a formal concept then it must meet all of the guidelines and rules required to fit the concept or it is not included in the category.
For example, for something to be an equilateral triangle it must have equal side length and all angles be 60 degrees. This is the formal concept of an equilateral triangle. If a triangle doesn't have equal sides and 60 degree angles then it doesn't fit the criteria or guidelines to be an equilateral triangle and therefore would not be included in the concept.