The audience of Michelle Obama's Commencement Address is primarily the graduating class of 2013 and their families, whom Obama also makes direct references to several times during the speech.
The speech was also televised, a full transcript was published on the official website of the White House, and it was referenced and quoted in numerous newspapers. Consequently, the wider audience is really much larger.
Obama's target audience seems to be all Americans, but particularly young people who are faced with the choice of whether to get an education or not, as well as anyone who might have an influence on such young people:
No matter what career you pursue, every single one of you has a role to play as educators for our young people. So if you have friends or cousins or siblings who are not taking their education seriously, shake them up. Go talk some sense into them. Get them back on track. (ll.237-244)
She also addresses her speech mostly towards ...