Most software engineering interns at Microsoft will be placed on a team of engineers that have several somewhat back burner projects that they think will take about 12 weeks or less to complete and that are of a moderate difficulty. Usually they are things the team would like to get to but are relatively low priority so they haven’t had the time to do so. I worked on building a natural language processing assistant bot for an internal tool.
It depends heavily on the team. Most often, you will be working on a side project that is related to what your team is doing. During my last internship, I worked on a virtual machine extension written in Go that's hosted on GitHub.