Authentic learning is learning in the "real world". It focuses on authentic deeds and students get to solve complex problems and find their solutions using a variety of activities like: role-playing, case studies, and collaborative peer learning. Authentic learning is idiosyncratic in its nature in that the setting where it takes place is multidisciplinary. In other words, the learning environment can be accommodated to foster different learning events.
Now with the widespread of web technologies, more and more environments for authentic learning have been created. Think of the virtual learning communities or what James Paul Gee called affinity spaces. These are ideal places where learners become "cognitive apprentices" to experts in the field. In this sense, to learn Math, for instance, students need to apprentice themselves to mathematicians. Not only that, they also need to take on another identity different from theirs which is that of the mathematician, the same applies to learning in other content areas.
Learning researchers have distilled the essence of authentic learning down to 10 design elements, check out this wonderful white paper to learn more.