Full Idea
A world w' is accessible to a consistent world w if and only if w' is possible in w. Being 'inaccessible to' or 'possible relative to' a consistent world is simply being possible according to that world, nothing more and nothing less.
Gist of Idea
A world is 'accessible' to another iff the first is possible according to the second
Source
Nathan Salmon (The Logic of What Might Have Been [1989], IV)
Book Reference
Salmon,Nathan: 'Metaphysics, Mathematics and Meaning' [OUP 2005], p.140
A Reaction
More illuminating than just saying that w can 'see' w'. Accessibility is internal to worIds. It gives some connection to why we spend time examining modal logic. There is no more important metaphysical notion than what is possible according to actuality.