In-universe, there was never an explanation. In fact, it was a plot point that House was driven rather crazy trying to figure out "what he missed". He was sure there must have been signs that Kutner was planning on committing suicide and he just didn't see them. This led to issues with his sobriety, etc.
Out on universe, there's a much easier answer. The actor who played Dr. Kutner (Kal Penn), had just been appointed to a position in the Obama administration. He had been a vocal advocate for Obama during his first campaign in 2007-2008, and in 2009 he was appointed Associate Director of the White House Office of Public Engagement. This required him to quit his television job rather suddenly, and the show decided to write him off in a surprising fashion.