icktoofay's technique is called a closure. There's an excruciatingly comprehensive discussion of closures here. I find them super useful for scheduling events with window.setTimeout(). They basically allow you to load up a function object with preconditions and then evaluate it with no arguments. Pretty nifty.
However for all their novelty closures can usually be avoided. For instance, if .beaver's are children of #group_beaver you would be better off with something like
function mouseOver()
{
$(this).children().fadeIn(100);
}
In event handlers jQuery makes sure that this always refers to the element that triggered the event, so you've basically got an argument for free. Given the simplicity of your example I'm guessing a closure is not necessary.
You could also do:
$('group_beaver').mouseenter(function() {
$(variable).fadeIn(100);
});
Which is really just a closure in disguise. Its the same as writing:
function mouseOver(variable) {
return function() {
$(variable).fadeIn(100);
}
};
$('#group_beaver').mouseenter(mouseOver('.beaver'));