The beta version of Vocaroo works the same way as the classic version just without the annoying step of enabling Flash. As you can see in my demo below, just go to the site and click record to start recording your audio. When you're done recording you can download an MP3 or embed your recording into a webpage.
Applications for Education
One of the ways that I've used Vocaroo over the years is for recording substitute teacher plans. I simply record my directions for the day and then post them either on my classroom blog or in Google Classroom.