I am confused when to use the period before the class names when referencing them. In this example why does the first use of the \'active-slide\' class use a period beforehand w
The . character is a selector. It allows you to select ALL DOM elements with that ('active-slide') class.
The jQuery syntax $('') uses selectors to return jQuery wrapped elements.
When you are adding/removing classes, you are not using a selector. You are literally removing a classname which is actually 'active-slide' (no .)
$('.active-slide') is using jQuery's element selector. (add|remove)Class('active-slide'); is modifying the element.