Doesn't damage any computers, no. The way a DDoS attack is set up though ... CAN involve a lot of computers (like yours) that have been "compromised."
If you open emails from people you don't know and click on links or attachments inside of the email, you can get yourself a virus, trojan or worm ... INSTALLED on your machine. Then that installed program can be used by a remote controller to launch DDoS attacks against some site.
The controller is called a "bot herder" and he gets reports sent back to him from infected computers. That lets him know just how many "zombie" or slave computers he has to work with.
If/when he has enough zombies ... and he wants to launch a DDoS attack on some website ... he sends a signal to all the zombies to connect with that site ... REPEATEDLY. A thousand computers trying to connect with N54 over and over ... causes N54 to slow down so extremely that real people like you and I simply can't "get in" to have our own page view requests answered. That means we sometimes CAN connect (when we luck out) but most of the time we have to wait and wait and wait ... and nothing happens.