It is important to realise that the IP addresses of devices on your local network are not directly accessible from the internet. These addresses are private, and are completely invisible from outside your local network.
Your ISP (Internet Service Provider) provides you with a single public IP address. This address is part of the internet.
Your local network is a LAN (Local Area Network), while the internet is a WAN (Wide Area Network).
Your router, as the only device connected to both the LAN and the WAN, acts as a gateway between these two networks. When a device on the LAN needs to connect to a device on the WAN, it must go through the router. Conversely, when a connection arrives from the WAN, the router is responsible for forwarding this to the appropriate computer on the LAN - this is called port forwarding.
Your ISP will provide you with either a static or a dynamic public IP address:
This means that your public IP address on the internet never changes. This is ideal, as it means you can always access your system using the same address.
Most ISPs give you a dynamic IP address. This means that your IP address can change from time to time. In this case, you will need to use a Dynamic DNS service to provide your system with a static host name that will always point to your public IP address, even when it changes. SecuritySpy has a built-in Dynamic DNS service, described in Setting up your Mac.