There are a couple of things here. The $() function is actually an object, like all javascript functions. This may be confusing, so if it is, ignore that part 
If you do
$('#someElement').click(function() { alert('foo'); });
, it binds the function you declared in that .click() to happen whenever the user clicks on #someElement. That's called "binding an event". The Events link you just posted has the list of available events.
Note that $(...).click(...function...) is the same as $(...).bind('click', ...function...).
Next you have effects. Effects are functions that act on the selected items immediately. For example:
instantly hides the #someElement. For added fun, you can do things like:
$('#someElement').fadeOut(500);
to cause the element to fade from 100% opacity to 0%, then hide. Note that 0% opacity is not "hidden" - it is still taking up space on the page, you just can't see it. The "500" is the time, in 1/1000ths of a second, that the effect takes to complete.
Have fun!