The Internet is a network of networks. There are two fundamental types of computers on the Internet, servers and clients. A server is a computer specifically set up to serve its files (make its files available for viewing or download) to client computers. A client is any computer you use to access the Internet: desktop, laptop, handheld, cell phone, etc. The files a server makes available to your computer can be Web pages, videos, sounds, images, etc. For your home computer to be able to receive files or any data from a server, your computer must request this information. This happens when you enter an URL in your browser or when you receive an e-mail.
Any computer can be set up as a server or a client. Without proper safeguards, anyone can access the files on your personal computer when it is connected to the Internet. This is why a firewall should be used. A firewall is simply a way to protect your computer from having its files accessed without your permission. There are many kinds of firewalls and they have different capabilities.