Yes, Hypriot is an operating system optimized for running Docker and you’ll need to flash an image of it to the pi. You can read about it here.
You can follow the brewpi wiki instructions for flashing it to your SD card (here), or Hypriot’s own instructions (here, but slightly outdated). In fact, it wouldn’t hurt to first read through all three links posted above to familiarize yourself with the process before choosing one set of instructions and following them step by step to install.
You could also just install docker on raspian (I for example have my pi running the media-center os OSMC and have docker running in the background) but it might require some customized steps that would be hard to guide you through).