"Now is the winter of our discontent"

I often hear this quote but the other day I went to see Richard III and I realised it means the opposite of what I had always thought it meant. It's a kind of double negative.

Now is the winter of our discontent
Made glorious summer by this sun of York;
And all the clouds that lour'd upon our house
In the deep bosom of the ocean buried.
Now are our brows bound with victorious wreaths;
Our bruised arms hung up for monuments;
Our stern alarums changed to merry meetings,
Our dreadful marches to delightful measures.
Grim-visaged war hath smooth'd his wrinkled front;

"The winter of our discontent" is like "the summer of our content".