DDoS is attacking your websites from a lot of sources. There will be a flood of requests that your server can't handle it. It is more or less like normal traffic but spiked. Hosting companies have their own means of handling such spikes.
This can be due to any no. of reasons. Just for fun, show of strength or for asking money from your hosting provider. This sort of attacks are more common than attacks on individual website. But since your host is attacked, you will face it too.
2. Attacking a particular website
As @Jason mentioned, it mostly won't happen with small website. Not unless you annoy someone capabale of doing it . Sites like Facebook, Google or even Godaddy website can face this sort of attacks.
It is best taken care of them. They have their own hardware firewall to deal with such attacks.