The software engineer intern will work on real projects at Google. In my internship, I worked on a team that was developing an app. I was given the first week to learn the language being used and after that got bugs to fix and features to develop myself. Keep in mind that you're not going to be treated differently than others just because you're an intern. Expect to work on hard and relevant problems at the company.
Google has a wide variety of teams working on different projects. An Intern would be assigned to a project, something that can be done in 3 months with clear deliverables, and hosted (mentored) by a full-time engineer. Generally, an intern project includes solving a new problem, lots of algorithm talks, and once a solution is finalized, implementing it. Details are project-specific.
Software Engineering intern (SWE intern) is matched with a team and a host. The host would be the main contact person for the intern. Usually before the Intern arrives, the host should have a project with a defined scope planned out for the intern. The intern is expected to finish the project within his/her allocated time. Depending on what kind of interns you are, you will either work alone (regular tech intern) or in team of three or two (Engineering Practicum intern). The intern can feel free to seek help from other team members besides the host. In fact, it is expected that the intern will work closely with one other person on the team besides the host. So that's about it with the program: You get a project assigned to you by the host; you worked on that project either alone or in team of two or three people and asked for guidance and help from both the host and another software engineer; at the end of the internship, you are evaluated on your performance on the project. Now, your range of work varies greatly depending on what project you end up on. It can range from UI/UX stuff to machine learning or data visualization to very low-level stuff like OS, embedded system, etc.