Aerospace engineers usually work in designing aircraft or spacecraft and related systems.
On a day to day basis, it really depends on a particular job.
Some work in hands-on jobs that involve setting up experiments and testing different components. Some work in design which involves a lot of creative thinking and doing lots of analysis, running simulations etc.
Others, like myself, work in areas such as space system engineering, which is a discipline that ties all the different parts of a space system together. So I spend a lot of time writing requirements, talking to people working on different aspects of the project.