Without the DNS or "hostnames" or domain names, we would be left having to reference all endpoints of our internet connections by their raw IP addresses.
While some people (mostly cranks) occasionally argue that this wouldn't be a bad thing, the fact remains that this name-to-number (and vice versa) translation is necessary because it adds a level of abstraction that allows seamless changes in our internet endpoints and destinations. Take a look at this:
Without hostname and domain name labels, and a universal mechanism to map between the two, all applications would have to somehow acquire end-to-end knowledge of all their peers, servers, or clients.
There is also another aspect of the DNS, which has emerged relatively recently, that takes it beyond a protocol simply for mapping names to IP addresses and back. The DNS is now, and will increasingly be, used to publish metadata.
Because of its ubiquity and relatively light footprint, especially combined with DNSSEC to authenticate responses, the DNS lends itself well for publishing other data that applications and clients will be searching for. I am speaking specifically now of authentication, reputation, and encryption processes such as X.509 certificates, PGP/GPG keys, DNS-based Real-Time Blackhole Lists (RBLs), and response policy zones (RPZs). The relatively widespread adaptation of SPF and DKIM signal the early beginnings of these types of DNS applications.
In the future, I see more activity occurring in these fields. As organizations and individuals come to grips with "surveillance-as-a-fact-of-life" and other shenanigans (such as third-party Certificate Authority (CA) debacles), an inexorable move toward taking control over your own data integrity and privacy is taking place. Thus, we see DANE as a response to having to rely on (possibly compromised, or corrupt) third-party CAs. We see increasing adaption of encryption and privacy enhancement, utilizing more uptake of DNSSEC and more authentication credentials being deployed over the DNS.