Life is about give-and-take. They offered you the internship or research job. Know what they expect in return
Its hard to imagine the professor whose course you aced wanting anything more than your intellectual development and academic growth. Or for that matter, that researcher from XYZ corp., who offered you that juicy research internship, wanting anything more than working with you on your favorite dissertation topic. Isn't a student job or research internship more of the same grad school work, with money thrown in?
Please be under no such illusions. When you are offered money for work, you are in a job. Your supervisor has objectives in mind that she wants you to fulfill. Being aware of these objectives is the first thing you ought to do when you start your assignment. If you are lucky then your supervisor will discuss these objectives with you at the start of your job and write down your kpis (key performance indicators). For example, a conference paper and a prototype implementation around topic "ABC" for the 4 month internship. But often researchers/professors do not discuss these objectives overtly. Why? Because research tends to be open-ended and there are multiple diverse ways for a student to be successful (or not). The kpi then becomes a moving target - "they know success when they see it".
Still, there are things that make your supervisor happy. A simple way of figuring this out is to look up her previous professional activities (papers, patents, conferences/journals targeted, demonstration/prototypes shown in tech fairs, etc) and think of how your work can improve the record here. Another effective approach is to track down an ex-student who has worked with your supervisor and ask her for the "expectations".
So that was the easy part. Tangible results in black or white.But there are other things you can do to impress your research supervisor. First and foremost, challenge her intellectually. Ask questions and put forth ideas. Show a willingness to learn new stuff and bring that knowledge into the way things are done. R & D is about pursuing the new and eschewing the status-quo. There is no point in shaking your head on every idea your research supervisor brings up; you need to show that you are more than two hands and two legs! Its the intellectual input your bring that really matters.