A Distributed Denial of Service Attack (DDoS) or a Denial of Service Attack (DOS) is exactly what it says on the proverbial tin. It "denies" people access to a "service", in essence. It's a means to sabotage the website services of a given company so that their pages remain inaccessible to the public thanks to wave upon wave of forced connections that deplete its resources and cripple its servers. The main modus operandi of this attempt to take down websites is to make network or computer services inaccessible to the users who are supposed to access them. The reasons for doing so will vary from "hacktivist" agendas to the machinations of a bored black hat hacker.
Some might even do small-scale DDoS in order to test out server capabilities, but that's rarer than actual penetration testing attempts. DOS attacks are typically promulgated by multiple people or a single person in order to prevent a service or Internet site from functioning efficiently. 4chan... one of the west's largest image boards for a variety of topics or hobbies... is a regular victim of DDoS attacks that typically renders the site temporarily out of order thanks to its connections with the hacker group known as Anonymous and its own DOS-related shenanigans. There are even DDoS attempts that can outright destroy a service for an indefinite period of time thanks to the sheer scale of the attack.
When a website is down and you're in need of some answers, you should refer to the site owner's Twitter account to confirm that it's down and see if the technical difficulties are DDoS in nature. He should be able to confirm whether or not he's being attacked by a DDoS flood. With that said, if you're hit by a DDoS, then you must know the signs and symptoms of such before being able to deal with it effectively. You should not confuse DDoS attacks with disconnects. Just because you're disconnecting from a match when playing your favorite game, your ISP is running slower than usual, or you're experiencing lag, that doesn't mean you're undergoing a DDoS attack.
Those are mutually exclusive problems that have no connection with DDoS. As long as you're able to reconnect and resume your activities or resolve it by switching ISPs and whatnot, then you're assuredly not being DDoS'd at all. One thing that you should take note when it comes to DDoS attacks is that they start slow and then escalate to a point where Internet access isn't possible at all. A DDoS happens whenever you, your computer, or your website servers are being hit with a huge amount of "Internet packets" at a fast pace that depletes your resources.