In mathematics, the term well-defined is used to specify that a certain concept (a function, a property, a relation, etc.) is defined in a mathematical or logical way using a set of base axioms in an entirely unambiguous way.
The concept of well-definedness is important for mathematics and sciences not to rely on human intuition, which is subjective and imprecise. For example, you might say an object can have the property of being "red"; however, this property is not well-defined because there is a wide variety of colours that some individuals would perceive as a shade of red, while others would insist that it is orange. Such a property would only be well-defined if strict rules were laid out that determine what frequencies of visible light the object were allowed to emit or reflect for it to be "red".
Another example would be that most people would certainly agree that 6 is almost as much as 7. However, there is no clear boundary as to where almost as much begins or ends. (There is, however, a well-defined notion of infinite sets being almost another.)
