If you are some one who would like to share your thoughts and sayings with everyone on Facebook even who is not your friend then you can use the Public Post option.
This option allows you to start your own following of people who are interested to see what you post. Not only that this option is good in those cases where you dont want to share you personal information and details with some one you dont know by adding them as a friend but you are happy to make them follow you and view your posts as that is the only thing you would like to share with them.
Public posts can be termed as your own mini blog where people can like and react to your posts as well as comment on them and start a discussion on them. You can also control whether you want a discussion with the general public on Facebook or just friends of friends.
If you have your own personal website you can also place a Follow button on it thereby allowing people to follow you.
You can enable this option by going to Settings -> Public Posts. Once you enable it people will start seeing the Follow button on your profile page along with the Add Friend and Message buttons.
Hope the above helped.