In general English is means that a situation “cuts both ways”, i.e. both good and bad consequences.
In Scripture, however, it is used is a different context. A double edged sword, obviously, has sharpened edges on both sides of the sword as opposed to one. Thus it is much easier to cut and penetrate with.
The Scriptures often refer to the Word of God as a double edged sword. It means that the Word of God penetrates our souls and cuts through our excuses and sins.