A discovery draft is a strategy for coming up with or developing your ideas. A discovery draft is similar to freewriting in that you can write freely, ignoring the structure and the full development of your ideas for the time being. You can also forget about matters of grammar and style.
But writing a discovery draft is different from freewriting in that a discovery draft makes a conscious attempt to focus on and to develop an idea or cluster of ideas. In other words, a discovery draft is like freewriting with an agenda. Because you have an agenda, discovery drafts tend to be more structured than freewritings.
Think of writing a discovery draft as writing a letter to a friend about your paper. You might first summarize for your friend's benefit what the assignment is -- “I have to write a paper about the Stanford Prison Experiment and how Carol Gilligan’s ideas, etc., etc.” -- and what problems you think you might have fulfilling it. You might address and then work out any confusion that you have about what your paper should say. You can write down what incidents in the webpage/video about the SPE are most vivid in your mind, and then try to figure out why those particular incidents are so vivid. In writing the discovery draft you might have an "ah-ha" moment, in which you see something that you hadn't seen before. And you break off in mid-sentence to explore it.
In a sense, the "ah-ha" moment is the point of the discovery draft. When writing the discovery draft, your thoughts are focused on your topic. You are giving language to your questions and observations. In this process the mind almost always stumbles across something new - makes a discovery. But if you DON’T have this kind of “ah-ha” moment, don’t worry too much about it – just write out whatever thoughts you have about what you’re going to say.
A discovery draft should consist of at least as many problems, questions, and “maybes” (“maybe I’ll say this, maybe I’ll say that”) as it does answers.