jQuery: Remove class from siblings

The issue is that siblings works for elements under the same parent. Your a links are not under the same parent since each one is wrapped in a h3.

So I believe this is what you want

$(document).ready(function(){

    $(".accordion h3:first").addClass("active");
    $(".accordion a:first").addClass("active");
    $(".accordion p:not(:first)").hide();

    $(".accordion h3").click(function() {
        $(this)
            .addClass('active') //set the current as active
            .siblings("h3") //find sibling h3 elements
            .removeClass("active") // and remove the active from them
            .end() // return selection to the current element
            .next("p") // find the next p
            .slideDown("slow") // and show it
            .siblings("p:visible") // find the other visible p elements
            .slideUp("slow"); // and hide them

        $(this)
            .find('a') // find a under current element
            .addClass('active') // and add active class
            .end() // return to current element
            .siblings('h3') // find sibling h3 elements
            .find('a') // find their a elements
            .removeClass('active'); // and remove the active
    });

});