Fundamentals
An attack that floods a website or service with so much traffic that real users can no longer reach it.
Formal
An attack that aims to make a system unavailable by using up its capacity, often by sending huge numbers of requests from many machines at once (a distributed attack, DDoS).
In plain English
Thousands of fake customers crowding a shop's doorway so the real ones cannot get in.
In practice
On election day, a municipality's website is hit by traffic from thousands of hacked devices and stays down for hours, until its hosting provider turns on filtering that drops the fake requests.
Why it matters
No data needs to be stolen for the damage to be real - a business that cannot serve its customers loses money and trust.