In Group theory proofs what is meant by "well defined" What is exactly meant or required for a mapping to be well defined? I was reading the First Isomorphism theorem (link), and the first thing the proof does is define a map and find out if it's well defined.
Intuitively it makes sense, but what are the requirements for a map to be well defined? For example in the link given, I understand they show one-one relationship as being well defined and later on they again prove it's injective.
What have I understood wrongly?

Say you have an equivalence relation $\equiv$ which defines equivalence classes $[a]=\{b | b\equiv a\}$. 
A function $F$, which is defined on elements,  will be well-defined, as a function on the equivalence classes if $F(a)=F(b)$
whenever $a\equiv b$.
