Public IP addresses are allocated (by an organisation called RIPE) to ISPs in blocks, so if you have neighbours using the same ISP it's possible that they'll have IP addresses close to yours.
The use of 192.168 addresses is there to provide a range of non-public (NAT - Network address translation) IPs that can be used repeatedly on many different LANs, a LAN with internet access will have 1 or more public IPs, then you use NAT to create an internal network. access to the internal addresses is handled by the router. when you access the internet, the webserver (or whatever you're accessing) sees the request coming from the public IP address of your router, when traffic is returned, the router knows which PC on the LAN sent the request, so forwards the data to it. a NAT IP is inaccessible from the outside world unless the router is configured to forward the incoming traffic to an internal address on the network
There are 3 reserved ranges of IPs for use on private networks, the one you choose usually depends on the size of the network as each range has a different amount of available IP addresses:
10.0.0.0 --> 10.255.255.255
172.16.0.0 -> 172.31.255.255
192.168.0.0 -> 192.168.255.255
Routers Are generally preconfigured to use 192.168. range as it's the smallest range & it's highly unlikely that a home user would ever need more than is provided by that range.
There's much more to it, but that's about as basic as I can make it