The DNS (Domain Name System) is a decentralized naming system that is used to translate human-readable domain names into IP (Internet Protocol) addresses. It plays a crucial role in the functioning of the internet as it allows users to access websites using domain names instead of remembering the complex IP addresses.

The correct answer to the given question is option 'C', which states that the DNS maps the IP addresses to a hierarchy of domain names. Let's understand this in detail:

Hierarchy of Domain Names:
The DNS organizes domain names in a hierarchical structure, known as the Domain Name System hierarchy. This hierarchy starts from the root domain at the top and extends downwards through various levels, such as top-level domains (TLDs), second-level domains (SLDs), and subdomains. Each level in the hierarchy represents a different part of the domain name.

- Root Domain: At the top of the hierarchy is the root domain represented by a single dot (.). It is the starting point for all domain names and represents the highest level of the DNS hierarchy.

- Top-Level Domains (TLDs): Below the root domain are the TLDs, which are the highest-level domain names. TLDs can be categorized into two types: generic TLDs (gTLDs) like .com, .org, .net, and country-code TLDs (ccTLDs) like .uk, .us, .in.

- Second-Level Domains (SLDs): Below the TLDs are the SLDs, which are the next level in the hierarchy. SLDs are more specific and typically represent organizations, businesses, or individuals. For example, in the domain name www.example.com, "example" is the SLD.

- Subdomains: Subdomains are additional levels that can be added to the hierarchy. They are used to further divide the domain name and can represent different sections or departments within an organization. For example, in the domain name mail.example.com, "mail" is a subdomain of "example.com".

Mapping IP Addresses:
The DNS maps IP addresses to the hierarchy of domain names by using a distributed database system. When a user enters a domain name in their web browser, the DNS server is responsible for translating that domain name into the corresponding IP address.

The DNS works in a recursive manner. When a user requests a domain name translation, the request is first sent to a local DNS resolver (usually provided by the Internet Service Provider). The resolver then queries the DNS server hierarchy starting from the root domain and traverses through the TLDs, SLDs, and subdomains until it finds the authoritative DNS server for the requested domain name.

The authoritative DNS server holds the mapping information for the specific domain and returns the corresponding IP address to the resolver. The resolver then caches the IP address and returns it to the user's browser, allowing them to establish a connection with the web server hosting the requested website.

In conclusion, the DNS maps IP addresses to a hierarchy of domain names, which is organized in a hierarchical structure starting from the root domain and extending through TLDs, SLDs, and subdomains. This mapping allows users to access websites using human-readable domain names instead of complex IP addresses.