Because of convience, many people when they wish to connect to their switch for administrating something, they simply telnet/ssh to the IP address that is assigned on the native vlan of the switch. (Or, if it's a L3 switch you can connect via ANY vlan that has an IP address configured on it)
However - one danger of this method occurs when/if that VLAN is having a broadcast storm. If you're accustomed to connecting to your switch via the VLAN.2 IP address and VLAN.2 is having a storm, then you're screwed because the storm congests the VLAN so much that you can't reach it, making it impossible to connect to your switch to fix.
The Managment interface allows for an administrator to configure an IP address on it that is on an entirely different network. This way, if VLAN2 with an IP of 192.168.1.10/24 is down for whatever reason (storm) - you can ssh/telnet to 192.168.2.10/24 that's assigned to the management interface of the switch and still administrate "i.e. Manage" it.
I know I just gave a single reason with a simple scenario, but I think it suffices.