If the destination is a neighbor, then a frame is created using the recipient's MAC address as the destination field. Otherwise, the router's MAC address is used. In either case, the IP packet header will include the recipient's IP address in the destination field. Technically, DNS is not required for IP to work. However, in practice the Internet would grind to a halt without it.
Human beings are simply better at remembering names than numbers.
DNS provides a distributed database that maps host names and IP addresses. The downside is that applications often fail when names cannot be resolved. Since most software is written to work with either names or addresses, temporarily substituting IP addresses for host names can be a useful debugging technique and also a workaround for DNS problems. A datagram can be thought of as a postcard and the network as the postal service. A postcard has sections for the recipient's address and a brief message.