We have a stipulative definition any time a word is being defined for the first time or in a brand new way. Stipulative definitions are in a sense completely arbitrary this means that they are basically non-binding proposals which no one needs to assent to. Stipulative definitions may be too complex, too obscure, or too unclear, but they cannot be judged true or false, accurate or inaccurate. Stipulative definitions simply are, and we can agree to use them for the purpose of argument or we can reject them.
Here is an example of a stipulative definition:
I suggest using apatheist to refer to people who disbelieve in gods (atheists), but who also dont really care about whether any gods exist or not (that is to say, they are apathetic about the question).
If stipulative definitions are so arbitrary, why are they ever used? There are a number of good reasons. For one thing, it might simply be a matter of convenience a way of using a single word instead of a couple dozen. Just because no one else ever uses the word in that manner doesnt mean that it isnt useful in some particular context. Very large numbers, for example, are sometimes given strange names like googol or yotta becuase those are short and memorable words which are far easier to use than the numbers written out, even in mathematical notation.
Stipulative definitions might also be necessary to clearly communicate some new idea or fact. If a new animal is discovered, of course a new name will be coined to refer to it. When first used, the name is neither right nor wrong. Once accepted in the scientific community, however, it ceases to be a stipulative definition and becomes something else: a lexical definition.
More: What are Definitions?