VPN stands for Virtual Private Network. Without getting into the details, it allows you to very securely connect to another network, and things will behave as if they were on that other network. There is an emphasis here on security. Through tunneling and encryption and other techniques, a VPN allows a connection to be extremely secure.
There are two main implementations for a VPN in most small to medium sized businesses. In one case, you have the site to site VPN. This might mean that you Have a main office and some much smaller branch offices. You very well could have the business need for a server in your main office, but not a server in each branch. By setting up a VPN tunnel, these branch offices can access all of the same network resources as if they were on location at the main office. The beauty of it is that the users can not even tell a difference. They will be able to access shared drives, printers, etc. This is a more permanent solution that requires no action by the users. It is implemented by using a hardware and software configuration, and once going through an initial setup, requires no further action.
The second implementation is probably more along the lines of what you are familiar with. This is the user to site implementation. It is what you would do if you were to work from home. This setup also requires some hardware and software at the site, but only software for the user. I won’t go into specifics on the software, as there are many options that vary based on your needs. The user simply launches their VPN client (I am a fan of OpenVPN) and connects to the office. Once the connection is completed, their computer will behave as if it were on the network. They would have secure access to shared drives and gain the ability to remote in to computers.
The advantage of using VPN is to reduce costs and increase flexibility. WIthout using a VPN, you would need to have a physical connection between two or more branches. This isn’t so terrible across short distances, but when you being to measure in distances it becomes quite prohibitive. It also allows your employees to work from remote locations; meaning you can use more, smaller branches to cover a wider area; it also means that you can allow some employees (or yourself) to work from home on occasion.
Give some serious thought to allowing your network to accept a VPN connection. For something with no drawbacks, low overhead, and ubiquitous implementation around the world, there is really no reason for you not to have the capability.