Forget college applications—Plato's forms have nothing to do with paperwork. The forms are what Plato believes to be true reality. Suspicious of the imperfections in the world around us, Plato challenges the idea that what we see in front of us with our own eyes is truly real. Instead, he thinks this world is a collection of imperfect copies of perfect objects, concepts, and ideas called the forms.
Let's take a classic example: the chair. You know a chair, right? Right. So, our world is filled with all kinds of different chairs: big chairs, small chairs, uncomfortable chairs, plastic chairs, E.T. the Extraterrestrial chairs—but up in the world of the forms, there's just one completely perfect chair, and all the chairs in our world are poor imitations of that one perfect, true, chair.
While this may sound wacky, Plato's theory of the forms helps clear up the pesky philosophical problem of universals. Or, in plain English: considering how radically different so many versions of a chair can be, how is it that we are still able to recognize them all as chairs? For Plato, the answer is that up in the world of forms, this one perfect chair represents "chairness" itself, the mysterious quality that makes all chairs chairs, even if one is pink and squishy, another green and prickly. This is why the forms are Plato's representation of truth: they are the true essence of everything we see, know, and think.
For Plato, the forms are a big deal because understanding what they are is the true goal of all philosophy. And while contemplating the true nature of "chairness" may sound a little nuts, remember that what Plato is really concerned with are things like "justice" and "the good." You can imagine that knowing the true essence of these things—and not just the imperfect versions we have—might be pretty important.
In fact, the form of the good is especially important for Plato since it works a little bit differently from the way other forms work. The form of the good is kind of like a super form, since it is what enables all other forms to be understandable. In other words, you can't understand anything if you don't understand the good first, since the good is at the basis of everything.
Plato compares the form of the good to sunlight, which makes things visible and keeps them alive. For this reason, the form of the good, more than any other form, it the most important goal of philosophy. Unfortunately for us, it's also one of the most confusing and complex of the forms, so don't be frustrated if you're not entirely getting it: even Plato scholars struggle with it.
What we know for sure is that Plato thought knowledge and goodness were totally connected, and it's his theory of the forms that helps him illustrate this crucial link.