He unified factions of Denmark with those in Norway much like how the technology we use today unifies different electronic devices. The Bluetooth logo is also a combination of the Nordic runes for his initials—H.B.
As for how he got his nickname in the first place is up to debate. Some sources say that he loved to eat blueberries, which permanently stained his teeth blue. Others speculate that he had a dead tooth, which had a dark blue/grey colour.