I don't know if I've ever really understood this quote myself. But if you take 'insanity' broadly to be making irrational decisions, addiction definitely affects rational judgment and impairs your control. My thoughts and behavior were in no way rational when I was at my worst, with all the ways I convinced myself it was okay or a good idea to drink/use again.
I never learned to 'manage' it, most people learn from their mistakes which cause them pain but I didn't. Intellectually I knew that what I was doing wasn't good for me but I still kept putting myself through the same thing. Most people learn from the mistakes that cause them bad consequences or pain but I didn't for a long time. It can apply to a whole range of dysfunctional relationships, cycles or behaviors.
Last time I went into recovery after a long series of relapses, I think I'd pretty much given up having any expectations, I just tried to focus on each day as it came. It may have helped relieve some of the pressure I'd felt previously though. I was willing to try anything and tried to be more open minded and receptive to people who knew what they were talking about, as I couldn't seem to trust my own thoughts or judgment at the time. Very glad now I didn't give up on recovery even with all the ups and downs along the way.