First of all, congrats on the offers! Definitely a good problem to have in terms of deciding where to go.
As far as securing an offer goes, there's three things that I think you should account for during your internship.
1) Mistakes are inevitable throughout the summer. The main thing you'll be looking to do is avoid making big mistakes and avoid repeating the same mistakes. The expectations for your internship aren't for you to come in and save the company (if you do, then that's great) but rather for them to get to see you in a team and client environment in order to assess your performance and potential growth.
2) Building on my first point, consulting is a people-driven job and, because of this, a significant portion of your evaluation will come down to your fit with the firm. This doesn't mean networking non-stop; instead, you need demonstrate your ability to be a strong follower, leader, and client-facing intern who will not crack under pressure. At the same time, it helps if you are able to bond with your peers, client team, and overall office during your stay. In short, the team wants to determine if they can see you working with them for the long-haul.
3) Lastly, and many will probably say this to you, attention to detail is key. As mentioned in the first point, you need to minimize the impact of your mistakes as well as the frequency of mistakes you make. Treat each draft deck, slide, research paper, spreadsheet, etc. as a final version. By doing this, you'll provide a higher standard to your work which will speak volumes of you as a professional.
If something is unclear to you about any assignment, ask right away and never leave margin for error. Whenever you have time for more work, ask how you can help your team. If there isn't enough work or if you're interested in other initiatives / tasks, reach out to others within your network. It's things like these that make a difference.
Hopefully this helps and best of luck with your internship. Feel free to reach out if you have any questions.