Depends on what you mean by "publish".
For others to see your gallery, a computer somewhere needs to act as a web server for your gallery.
A common method for this is to have an account with an ISP that gives you disk space on one of their servers.
If you have a high enough version of your operating system, your personal computer may have the software needed to act as a web server.
If you just want your immediate family to see the images, you can save your gallery to your hard drive or local network and let other just open the root page using their web browser.