People reach websites by name, but the machines carrying the traffic route by numbers. The domain name system is the directory that translates a readable name into the numeric address of the server behind it, performing this lookup constantly and invisibly before almost every connection.
It is distributed and layered, with many servers sharing the work and caching answers so repeated lookups are fast. Because so much depends on it, problems here can make services seem down even when they are running fine, which is why its reliability is quietly critical.