What is a DDoS? A DoS attack is a Denial of Service attack. An attacker on the internet sends a lot of traffic to a victim who didn't request the traffic. The victim needs to deal with the traffic somehow. The victim will either block traffic with the originating address of the attacker at his end device (like a PC or TV) or further along the route the traffic takes to reach the victim, like at the victim's ISP.
A DDoS attack is a Distributed Denial of Service attack. The attacker compromises many internet-connected devices (like TVs, webcams, Windows machines and other small devices people forget to keep up to date, like routers). The software the attacker then runs on these devices are called bots (from robot, just signifying that they are programmatically automated; you get good bots too).
A network of these bots is called a bot net and they are controlled by command & control (C&C) servers.
Commonly botsnets are, these days, controlled by APTs (Advanced Persistent Threats, which are long-running entities that are well staffed, commonly funded by governments).
There is a part of the internet known as the Dark Net which mostly just means part of the internet not commonly visible on the regular World Wide Web in your browsers. If you ever want to explore it, use a tool called Tor, but be warned, you can easily do things that is criminal on there, so be careful not to do so. On the Dark Net you can buy and sell all kinds of things like drugs and even murder for hire, but also the services like these DDoS attacks from those who control bot nets. Now keep in mind that they cost serious money at the scale of this DDoS, so you have to consider what motivates someone to buy or run one. In most cases these days they are used to hide more serious direct attacks, like hacking. When you find a vulnerability in software that nobody else knows about that vulnerability is called a Zero-Day (Zero days since the creators or the world have been aware of it and can fix it). These are very valuable and also traded on the Dark Net. You can probably get $2 mil for a full Android phone compromising vulnerability (though Google now offers more money in a bounty program if you let them know first).
APTs collect Zero-Day vulnerabilities and when they have a target they need to execute an attack on, they use their C&C servers to control a bot bet; They may use DDoSes to hide the attack. Bet you never thought you'd understand a sentence like that! ;-)