New hires tend to focus on the immediate things – running errands for their boss, doing little projects quickly, helping out on ad hoc tasks, and doing things whenever they pop up. While there is nothing wrong with any of those things (you should always be trying to do whatever you can to add value), no one will remember you for it. What you need to focus on is leaving your mark.
Leaving your mark means developing something over your internship that will persist beyond your stay. It might be a new system, a new way of handling orders, a new way of assessing market opportunities, a new way of greeting customers – whatever it is; it will last beyond your tenure at the firm.
In essence, your internship should consist of a few major projects (most likely only 1-2) and many many minor projects surrounding those. If your internship was a painting, the minor projects would make up the background – the trees, the grass, some water, the sky, the clouds – they aren’t individually worth talking about, but they make up a major portion of the painting. Your major project(s) would be the foreground – one or two well painted individuals that would stick with you after viewing the painting.
The Sistine Chapel is a major painting, but the only part of it most people remember is the image of God touching Adam with fingers outstretched. Everyone remembers that the entire ceiling painting is breathtaking, but they only vividly remember that section – this is the same effect that internships take on. How you handle the minor and major projects will define what people ‘think’ about you – but when discussing your overall success, you must make sure they have one or two major projects to point to that define your success.