From good old Wikipedia -
DIMINISHED RESPONSIBILITY - In criminal law, diminished responsibility (or diminished capacity) is a potential defense by excuse by which defendants argue that although they broke the law, they should not be held criminally liable for doing so, as their mental functions were "diminished" or impaired
I, personally, think this word out the above sentence, sums up perfectly what 'diminished responsibility' means!!!
Yes, there are certain times where these cases are genuine, but they are very very rare. More and more 'criminals' are claiming mental illness, depression or whatever. I've very recently seen close hand that mental illness is just an excuse. I'll try nd dig out the article from the P&J and let you judge for yourselves later...