Denail of service attacks cuts off access to services and information. If it's done to an internet based company like amazon or ebay, they loose buisness and lots of money from wasted bandwidth that they are paying for. Distrubuted Denail of Service or DDoS attacks use many machines to attack one. Some like, SYN Connect attacks, abuse the way computers recieve tcp connections, the 3 way handshake. Smurf attacks use forged hosts in icmp packet headers. So they can be sent out to millions of machines and they all return to the victim computer flooding it with responses, when it never made the requests in the fist place. They abuse other faults in the way TCP/IP works. To understand them you first need to understand TCP/IP.
Others abuse the actualy defects in the hardware itself, like the ping of death. It sends the command to hanf up to your modem, +++ATH0. Some abuse faults in server programs with buffer overflows which can also be used to exploit systems. If you want to understand all the defects of a system you should understand how that system works first.