Network servers have devices on them known as ports. Each port is set up to understand a certain type of language. There are ports, for instance, for database applications, website content, e-mail, instant messaging/chat, etc. They are similar to channels on television or a CB radio. Each port is either open or closed to the outside world, meaning it will "listen" to requests for that type of service. If a port is open, it is an opportunity for a hacker to attempt to access data or files on that server. Some ports need to be open, such as the port for web content on your Internet server. Others should not be (like the e-mail or database ports on the same server). Opening unnecessary ports can expose sensitive data and systems to hackers.
If hackers are able to access your network, the damage they can do is extensive. Depending on what parts of the server/network they reach, they could steal data, deface your website, or worse.
