Microsoft Azure essentially allows the provision of 'temporary' supercomputers on demand. It can be used to set up a high performance computing (HPC) cluster tailored to one's needs, limited only by the amount of money that can be spent. Other services range from web app hosting, storage and virtual machine deployment (e.g. more than 128GB of RAM), ranging from many options for both Windows and Linux.
In the course, everyone was given a generous £1500 to spend on Azure and most of the main features were explored in the examples given by Dr Takeda. For example, we used Azure to provision Windows Server and Ubuntu Server virtual machines and set up our own HPC cluster, on which we ran a computationally intensive Monte Carlo simulation (locally from within an iPython notebook). More details and screenshots can be found on my personal website, which is also deployed on Azure.