You need a server with web publishing software (Microsoft's IIS, ASF's Apache, etc.)
If the server is hosted outside your local network, you will need FTP access to upload your files to it.
Check with your ISP. They normally provide this service for free to their home customers for small web sites.
A reasonably cheap way of hosting your own website, is to use a Synology DiskStation. It has Apache, MySQL and PHP and is relatively easy to set up.
You don't need a server, you just need a web hosting package such as the ones from GoDaddy or many other hosts. You then send the web gallery directly from LR to your web space.
As you're asking such basic questions, it might be best if you read articles like this and see if a friend or colleague can get you started.