Update: Blizzard has tweeted that the DDoS attack is over. "The DDoS attacks from earlier have ended and players can now log into BattleNet. We are investigating reports of World Server Down in WoW," the company tweeted.
We continue to actively monitor an ongoing DDOS attack against network providers, affecting latency/connections to our games. #BlizzCSAugust 3, 2016
Although it's impossible to know for certain, a hacking group by the name of PoodleCorp has claimed responsibility for the attack. Neither the group, nor anyone else claiming responsibility, has given an explanation for the attack, though Blizzard did hand out a lot of Overwatch bans earlier this week.
Or else, it could deliberately coincide with the new "Summer Games" season, which introduced a special Lucioball game mode to the FPS. Whatever the case, we'll update as news comes to hand.