The first set of work helps me understand that you can do the job. Secondly, I want to see you in your work. This is why another key part of a good portfolio is work that is more personal, experimental, and possibly less refined or polished. If you have work that you are obsessed about, work that keeps you up at night, I want to see it. Do not let labels get in your way — it does not have to be “design” to be included, it just has to be something you care deeply about. What work have you done outside of your design classes? Painting, sculpture, photography…all of it counts if it is important to you and your relationship to creative practice.
Finally, you should include the kind of work that you want to do more of, and you should leave out the work you want to do less of. You will get back what you put out — if you do not want to design websites, don’t put websites into your portfolio. If you want to design more book covers, make sure plenty of book covers are included. Having a clear vision of what you want to do as a designer is important, and your portfolio should reflect that in its content. It is always obvious to someone looking at your work which stuff you care about, and which stuff you don’t care about. Part of having an opinion about design is including work that matters to you, instead of including work just because you think that is what you are supposed to do. Always remember: it is not just a portfolio, it is your portfolio.