Secondary IP addressing uses multiple networks or subnets on the same data link.  By using more than one subnet on the same medium, you increase the number of available IP addresses.  The router needs an IP address in each subnet so that the hosts in each subnet have a usable default gateway IP address in the same subnet.  Packets that need to pass between these subnets must be sent to the router.

The biggest negative to secondary addressing is that packets sent between hosts on the LAN might be inefficiently routed.

Subnet Zero
IOS can restrict a router from configuring an ip address command with an address inside the zero subnet.  Subnet zero is the one subnet in each classful network that has all binary 0′s in the subnet part of the binary version of the subnet number.  In decimal, the zero subnet happens to be the same number as the classful network number.

With the ip subnet-zero command configured, IOS allows the zero subnet to become a connected route as a result of an ip address command being configured on an interface.

With the no ip subnet-zero command configured on a router, the router rejects an ip address command that uses an address/mask combination for the zero subnet.  The error message will say “bad mask” if you configure a zero subnet with that set.

no ip subnet-zero configured on one router does not affect others and it does not prevent a router from learning about a zero subnet through a routing protocol.  It simply prevents the router from configuring an interface to be in a zero subnet.