Mail servers receive mail, store mail, and keep settings. Each mailbox is assigned to a person or inbox, say firstname.lastname@example.org. The mail server allows a user to travel from computer to computer, and access the same e-mail. It also allows for web access, so if a user is not at their computer or one with their e-mail account set up on it, they can simply access the mail through a web interface.
DHCP stands for Dynamic Host Configuration Protocol. DHCP allows devices to be assigned to a network. For example, DHCP can automatically assign an IP address to a a device, there is a pool of IP addresses and the devices get one from DHCP or you can statically assign IP addresses based on MAC addresses through DHCP. Basically, it’s a DHCP is a way to add network devices.
DNS stands for Domain Name Service. DNS is a service that allows you to resolve domain names. For example, within an organization, each workstation is given a name, each printer is given a name, etc. These entries now match names with IP addresses in the DNS server. When a computer requests to speak to another workstation, “PC_2_OFF” for example, the originating computer sends out a request (as if in a browser or RDP client) to the DNS server. If the DNS server can match it with an IP address, it will redirect to the appropriate location.
Hope this helps!