Thanos2001,
I will try to keep this simple...I tend to write books. If your situation is typical, you have a "modem" (cable/DSL, etc.) and you have a router. Wired or wireless makes no difference.
Typically, you use a "private" network (also called a private address range) inside your home. For example, on a Linksys router, I think it defaults to using 192.168.1.* addresses. (It is that or 192.168.0.*).
Your ISP will provide you a single public IP address. Typically, this address becomes the external address of your router. It is the address that can be used from the Internet to route to your network.
If you want to host services, such as an FTP service on your NAS, you have to configure your router to point the traffic to the device. (The NAS does not need to know anything about the public IP.)
This is typically called "NAT" which stands for Network Address Translation or "Port Forwarding". In the Linksys router, the menu item is "Applications and Gaming". In it, you can tell your router that all TCP traffic on port 21 (FTP) should be directed to the IP Address of your NAS.
Once you enable this port forwarding, all normal FTP traffic from the internet to your public IP will be directed to your NAS.