Meaning of "defined" What are the precise meanings of terms "defined", "well defined" and "undefined", etc.? We can't define what "defined" means since then we would run into circular definitions. (If definitiveness is established in terms of something else like "existence", then again we face the same problem.)
 A: "Well defined" usually means unambiguously defined, which is necessary for the definition to be any good.  For example, suppose you're defining multiplication modulo $11$.  Observe that $6$ and $17$ are equivalent to each other modulo $11$.  Similarly $4$ and $37$ are equivalent.  So if I find $6\cdot4$ and also $17\cdot 37$, will those be equivalent?  Notice that the first is $24$ and that reduces to $2$ and the second is $629$ and that reduces to $2$.  If they didn't reduce to the same thing, then multiplication modulo $11$ would not be well defined.
"Undefined" refers to an expression, not to a value of an expression.  Thus "$20/4$" is an expression, and "$2+3$" is an expression, and they're two different expression, but both have the same value.  The expression "$0/0$" is also an expression, but it doesn't have a value.  Hence it is undefined.
What "defined" means in general is a tougher problem and I won't attempt to deal with it here unless the Muse get more emphatic.
A: Mathematics is not about what "define" means in English or a natural language - that is a subject for philosophy or for the study of language. But we can use natural language to explain what it means to define something in mathematics.
The most common type of definition in mathematics says that any object with a certain collection of properties is given a certain name. For example a polygon with three corners is named a triangle. These definitions are trivial in the sense that you could replace the defined word with its definition, and although it might be inconvenient there would be no formal loss of meaning. 
The term well defined is used in some settings where we want to make a definition, but there is a worry that the "definition" is faulty. It is used most often when we define a function on an entire equivalence class by looking at a representative of the equivalence class; in this case we have to argue that the function gives the same value no matter which representative is chosen, and we then say that the function is "well defined". 
