I assume that your gateway device to the internet does NAT (network address translation), i.e. your home network uses for example a private network like 192.168.0.* and you dynamically get one IP from your ISP which is used by the gateway.
In that case someone on the internet only is able to access port 80 on your home network web-server, when you have explicitly configured a port forwarding of port 80 to the web-server on your gateway.
Besides checking the gateway configuration you can also check it from a system with a different IP. Get the current external IP of your gateway and try to access port 80 from the other IP. And/or use
nmap on it.
On the LAN, on a linux system you can lookup the configured IP addresses via:
$ ifconfig | grep -A1 encap
eth0 Link encap:Ethernet HWaddr 01:02:de:ad:be:af
inet addr:192.168.1.1 Bcast:192.168.1.255 Mask:255.255.255.0
lo Link encap:Local Loopback
inet addr:127.0.0.1 Mask:255.0.0.0
In this example it is on the 192.168.1.* network, which is a private address range, i.e. one need a gateway that does NAT for internet access:
$ route -n
Kernel IP routing table
Destination Gateway Genmask Flags Metric Ref Use Iface
192.168.1.0 0.0.0.0 255.255.255.0 U 1 0 0 eth0
0.0.0.0 192.168.1.42 0.0.0.0 UG 0 0 0 eth0
Meaning that the gateway has the IP 192.168.1.42 on the LAN.
Usually all this is automatically configured via DHCP - where e.g. the DHCP server runs on the gateway device.
To get the external IP address of the gateway one can use the administrative interface of it or browse an internet site that displays it, e.g.
$ curl -s http://www.lawrencegoetz.com/programs/ipinfo/ | grep -A1 'Your IP'
<h1>Your IP address is<BR>
(don't know this service - via google you can find a lot of alternatives)