Suppose you run a ecommerce website, selling something, say books. at www.booksrus.com
A denial of service attack when when my computers send in zillions of requests to www.booksrus.com with such rapid volumes that I use up all of your computers and all processing slows down. Your site is still technically "up" but finding a book takes minutes instead of seconds, and using the cart to do a checkout takes a half hour. So all your customers give up.
The specifics of the attack vary. some address very primitive networking protocols, some the web server, some the business logic. The result is the same, no one can use the site to buy stuff.
a related topic is a "DDos" Distributd denial of Service attack. Here, the same basic thing happens, your server gets flooded and no real work can be done. The difference is that in the distributed attack, there may be thousands of bot computers attacking.