Think of the premise as a succinct but persuasive sales pitch, even if the only person you're selling an idea to is yourself. Usually, all you need is a short paragraph that highlights the purpose (from the designer's point of view) and potentially the value (in the player's eyes) of creating that particular piece of game content. If you have strong references do not be afraid to use them; these can be anything from movie scenes to screenshots of existing games.
It's common for the premise to change and evolve multiple times, especially as it's likely to be written down a long time before you actually get down to creating the described content. Nevertheless, it's always good to write down and present your ideas to other people ...
