I usually hear people say this when they are referring to anti-depressants or anxiety medicine. I believe that the drugs used to treat both of those do actually take some sort of edge of something off, but I struggle with wanting some "thing" to take the edge off of my discontentment or my irritability.
It's a difficult thing for me to confess that I want to turn to a drink or a pill or some sort of numbing device. It's a great thing that I don't turn to such impulses because of God's grace in my life keeping me from giving in to them. I just desire to be at a place where I allow God to take the edge off of my funk. For some reason I just don't believe that He will do it. I know that He freely gives us anything we need to avoid falling into such temptations. But, for some reason I compartmentalize Him in that I don't see Him offering some "thing" for me to take the edge off. My prayer today and in future days is that when I have the desire to self medicate, I will turn in submission to Him and allow Him to do what he wants with whatever edges I'm not happy with at that moment!