Hi nuggetinu,
You have some great questions at hand!
-what is address family ?
An address family stands for a particular format of addresses used by a routed Layer3 protocol, such as IPv4 or IPv6. In a routing protocol configuration, an address family specifies how the routing protocol will treat particular addressing information for IPv4, IPv6, or perhaps other address formats - whether it is going to advertise that information or not, and whether there are any specific settings related to it.
-when we use address family ?
With routing protocols that support multiple address formats, you need to use an address family practically every time you configure it, because you need to explain to the protocol what you want it to do. With EIGRP and named configuration mode in particular, do you want it to run over IPv4 and exchange IPv4 routes? If so, you need to configure the address-family ipv4. Do you want it to run over IPv6 and exchange IPv6 routes? Ifo so, you need to configure the address-family ipv6. Do you want both? Then you need to configure both. You actually cannot configure a named EIGRP instance without an address family because all IPv4 and IPv6 specific settings are put inside the address-family subsections; they do not exist directly under the router eigrp name anymore.
-why we use address family ?
It is a convenient way to have just a single configuration block for a routing protocol, and inside that configuration block, explain what we want the protocol to do for IPv4, what we want it to do for IPv6, and so on.
An alternative approach would be the old style configuration - router eigrp process-id for IPv4, and ipv6 router eigrp process-id for IPv6. Note that the old approach is also using address families - but they are not configured, rather, they are implicit - the router eigrp process-id is always tied to the IPv4 address family while the ipv6 router eigrp process-id is always tied to the IPv6 address family.
-what is the benefit of address family with eigrp v4 or v6 ?
This is really about configuration style. There is no benefit in terms of how EIGRP works. The use of address families is a particular style of configuration where, instead of configuring a set of independent (numbered) EIGRP instances, one for each protocol (IPv4/IPv6), we use a named EIGRP instance and configure its IPv4 and IPv6 specific settings under an address-family subsection.
BGP works in a very similar way - you might find this older post of mine interesting, although with BGP, situation is even more fancy since BGP can run, say, over IPv4 while advertising IPv6 prefixes over this IPv4 session; EIGRP does not do this for multiple reasons.
https://supportforums.cisco.com/t5/wan-routing-and-switching/when-to-use-bgp-address-family/td-p/1927840
Feel welcome to ask further!
Best regards,
Peter
