Raggedy,
Let me (on behalf of our team) firstly welcome you to Firewall.cx.
When one is keen on learning but discouraged from the people he is surrounded, its possibly the worst thing that can happen to him, as its like cutting the wings off a bird that wants to learn how to fly.
Don't worry though cause the team and members of this site will gladly spend their valuable time to help you and everyone else - that's why we are here.
Subnetting is a big topic, but also a very easy one once you learn how to tackle it. I am not aware of your experience, so I'll keep the explanation as simple as possible.
You mentioned that your ISP gave you a subnetmask of 255.255.255.240, and from your question, I am assuming that this subnetmask has also been applied to your internal network;
So what effect will the above subnetmask have in a network when it's applied ?
The purpose of using subnet masks is to partition (split) our network into smaller pieces, making it easier to manage and also increasing security access to specific portions of that network.
Small networks usually use the standard 255.255.255.0 subnet mask (also called - "default subnet mask") since they have a very simple structure and are rarely required to be partitioned.
I would not be able to answer you as to 'why' your boss has chosen to apply this subnet mask to your internal network (he might not be sure himself!), but I'll explain what it does.
The default subnetmask I mentioned above (255.255.255.0) will give your network the ability to host upto 254 hosts (computers) or if you like, IP addresses. This means you can allocate upto 254 IP addresses to this network.
The 255.255.255.240 subnet mask, when applied, will partition your network, that is, create 16 smaller networks, and each network will be able to have a total of 14 IP addresses.
Let's compare them to get the big picture:
Subnetmask 255.255.255.0 = 1 network with 254 usable IP Addresses:
(assuming 192.168.0.0 is our network)
Network 1 = 192.168.0.0
Range: 192.168.0.1 (first available IP) to 192.168.0.254 (Last available IP)
Subnetmask 255.255.255.240 = 16 networkswith 14 available IP addresses:
(Assuming 192.168.0.0 is out network)
Network 1 = 192.168.0.0
Range: 192.168.0.1 (first available IP) to 192.168.0.14 (last available IP)
Network 2 = 192.168.0.16
Range: 192.168.0.17 (first available IP) - 192.168.0.30 (last available IP)
Network 3 = 192.168.0.32
Range: 192.168.0.33 (first available IP) - 192.168.0.46 (last available IP)
Network 4 = 192.168.0.48
Range: 192.168.0.49 (first available IP) - 192.168.0.62 (last available IP)
Network 5 = 192.168.0.64
Range: 192.168.0.65 (first available IP) - 192.168.0.78(last available IP)
....and so on..
As you can see, we have smaller networks with fewer IP's in each one.
I'm hoping this answers your question, if not, just let us know specifically what you need clarified and we will provide the best answer for you!
Since it seems like your new to subnetting, we have one of the best tutorials available in the world (seriously). Check it out and I'm sure it will help you understand everything on the topic.
Cheers,