Independent studies allow the student to explore an academic opportunity or interest that is not available through regular coursework. What is unique about an independent study as opposed to a regular class is that it is uniquely tailored to your interests and academic pursuits. For example, if you are interested in one specific branch of philosophy, like moral philosophy (ethics), but there is not a class that focuses on just that, you can approach your academic supervisor and they will help place you in an independent study.
One of the nice things about having an independent study is that it is self-paced. It is not like a regular class where you meet two or three times for x-amount of time. Rather, you meet once a week, at a time that works well for both you and the professor, and the meeting can go for however long or short it needs to. This also means that there is not a rush to cover a certain amount of material each class. Instead, you go at the pace you are comfortable with. You are able to focus and go into depth on certain concepts that intrigue or confuse you. For example, in my independent study on biblical Greek, sometimes I need to spend 30 or 40 minutes on one passage. And what is really nice is that there is not that feeling of needing to be in a hurry or needing to nod your head as though you understand when in reality, you do not. Everything is set up at your pace; if you need to spend longer on one thing, it is okay and is encouraged.
Independent studies are great for developing a strong sense of responsibility.
In an independent study, you are responsible for coming to the class. You are responsible for doing the work, more so than in regular classes. In a regular class, if you do not do the reading for one class, you can stay under the radar and not participate for that class period. But in an independent study, you cannot rely on anyone else to cover for you not reading or doing the work because the nature of an independent study is that it is just you and the professor having a conversation, but you, the student, are leading it. If you show up to the independent study and you are not prepared, the professor will know it. You are responsible for all of your work.
An independent study also causes you to wrestle with the material more than a regular class does. It requires you to foster a questioning attitude rather than a passive accepting attitude. It forces you to be original in your ideas and arguments. If you do not agree with someone, you have to give your own reasons why. It helps develop your ability to think critically about the text.
Another wonderful aspect of having an independent study is that it gives you the ability to build a strong relationship with the professor when you otherwise would not have, as one student in a regular class of twenty or more. This allows the professor to gauge what your needs are as the student, and better conform to those needs. Instead of having a lecture, you have a conversation about something you both are interested in.
This student-professor relationship becomes more of a friendship because you both are studying and discussing something that you care about and are interested in. What better way to explore a subject than with a person who is more knowledgeable than you and who is also your friend?
Josh Steen 
Hannah Bonanducci 
Ella Curcuruto