You gain the capability to reach students which would not be able or willing to attend courses in the fixed time/place which your courses are currently available.
Currently I am a student at Harvard's Extension School. I have worked in the field that I am currently studying for over 15 years, and I am unwilling to step away from my career in order to pursue a degree. Hence any program that failed to provide a considerable amount of flexibility around physical location and time of day/ day of week scheduling were simply discarded from consideration.
Now having taken a variety of distance education courses over the years, I can tell you that there are good and bad ways to run distance education courses, just as there are good and bad ways to run a traditional course. Student faculty ratio is just as important in online courses as it is with in person courses. The 'personal' touch I received sitting in a lecture hall with over two hundred students in a Biology course was just as worthless as a similar number of students watching a lecture online. It quickly becomes clear in such circumstances that the staff does have the time or availability to really interact with the students.
If a professor is willing to invest the time and effort in an online course, there are several types of tools available to connect to students to ensure their understanding of the material at hand. The dirty trick in this is that it takes time and effort, just as it does when meeting in real life. The problem comes in when a school or a teacher come to think that the Internet is a magic wand which one will wave and everything will become better. Take my current course as an example. I have exchanges several messages with the Professor (mostly email, but not exclusively), in each instance I have received very thorough and timely. The assignments are not only well though out, the feedback is detailed and comes quickly.
To do this well takes time and effort. Those schools and professors that find a way to be successful in a new medium will likely thrive. Those that opt to treat distance education as a holding bin for warmed over leftovers will suffer.