Want a real life example of keywords? Let's look at nicknames and Facebook. Let's say a bunch of your friends decide to upload photos on Facebook. Now each of these friends calls you by a different nickname. So they tag you in them by whatever they call you. In order to see all of these pics, you'd have to search for each of your nicknames to find them.
Subjects on the other hand are like your actual given name. Or at least your Facebook official name. Now when you actually tag photos on Facebook, you know you're forced to tag them with their "actual" name. And while it may be less personal or descriptive, you do get all the photos of you when you use the offical name tag.
Keywords are simply those words you type into the search box to get the results you want. Just like in Google, you don't type your whole question, just the important words or terms that will help you get the answers. Remember to consider synonyms when you create your keyword list.
So what are subjects then? Subjects are a specific word or phrase some librarian has assigned to a particular topic. Basically it's a tag we attach to articles or books. Why would we do that? Because that way when you search for that specific word or phrase you get EVERYTHING that has been tagged with that term. You can find these subjects (or subject headings) in the library catalog and most databases (except JSTOR). Usually they live along the left side bar or in the middle of the record (when you click on a specific book or article).