I have seen people writing
$(document).ready(function(){
});
and some writing
$(function() {
});
$ is the jQuery object itself, which when called implements a whole pile of different interfaces. $('string') runs a selector or constructs a node; $(domElement) wraps an element... and $(a_function) is a convenient short hand for $(document).ready(a_function). See the jQuery API docs for (much) more information.
A note in passing: $(function () { ... }) is shorter, but if you ever want to search for all of your on-ready events, you might be wishing that you had .ready to search for :)