Port number are used as connection points internally in a machine in the operating system. Most of the time users are not concerned with port numbers but you may find helpful knowing a little.
The place most people will ever see something about port numbers is when browsing the web on the Internet. Web pages commonly use port 80 as the way they are transmitted across the network and when the machine receives them they come on port 80 which tells the machine it is a web page.
Now more and more we use secure web pages which means when the web page is sent across the web the information is sent encrypted. This means if someone steals the signal while in progress it all looks like garbage You want to do this when sending sensitive or personal information such as passwords, account numbers, etc. These pages use port 442 instead of port 80. As a user you can tell the page is using 443 instead of 8 in two ways. One is in most browsers by the address in the address box is a lock and if using port 443 it shows the lock locked. The second is if the whole URL shows it will end in :443 instead of :80. However usually the port number does not appear.
When you send email, you use port 25. This means the different things we do are using different routes to us. In some ways I think you could compare to normal life. If you get a letter, the USPS delivers it, but many packages come via UPS. Both are being delivered to you, but one uses white trucks with red and blue markings and one uses brown trucks. We use a different communication to talk on the phone.