I have a Mac Mini machine on top of which I have installed Virtualbox running CloudLinux(a variant of CentOS). While I installed Linux it had eth0(NAT): 10.0.15.1. I can ping to external network through eth0.
Aim: I am planning to provide web hosting service to Clients and therefore I purchased few public IP, DNS and gateway been provided to me.

I have recently installed Web Hosting software called plesk for managing billing stuffs, controlling the web hosting facility. I have got my domain name.
I added a new interface eth1 with one of PUBLIC IP(NAT) 171.x.x.x. I have added proper subnet, gateway. The issue I am facing is its not accessible from external world or even from the host machine (Mac here).

Am I doing anything wrong?

Please note my network configuration look like:Airport Extreme setup with dedicated IP, subnet and DNS; MAc Mini server connected by Ethernet to Airport Extreme.

you really shouldn't put these public IP's on actual (or virtual) kit. I'd strongly suggest you do this as a NAT operation on your edge router, which sounds like it must be possible. you mention "PUBLIC IP(NAT)" but imply the address is NOT natted, as it's on eth1. can you explain more about that? how are these public addresses being delivered? Usually it would be in the form of your ISP delivering a cable with a subnet on the end of it, they wouldn't route traffic *through* one of your devices.

Chris,

I have purchased them from service provider where the have provided me with gateway address, DNS domain, Public IPs.
Can you help me understand How usually we configure the public IP? Do we generally keep 1 interface just for public IP?

you bought these things from them, you *really* need to ask them, not us.