The NAT solves the issue of there being too many people using the internet and not enough IP addresses for everyone. It allows for many computers connected to the same router to share the same public IP address, by assigning each device connected to the router with a unique private IP address.
VPN (Virtual Private Network) allows for users to access private networks and share data from a public network securely. VPN's can be used for a number of reasons including: accessing data that is geographically restricted, or accessing websites that are censored in your area and accessing data securely without anybody watching.
Routers and switches are hardware devices that are essential to the running of networks.
The DHCP is responsible for assigning IP addresses to hosts on the network. DHCP is imperative to the running of the network, if DHCP was not used then IP world be allocated manually, this would lead to conflict occurring as two hosts would have the same IP addresses.