For starters let me state that I have no problem RTFM. I've spent the better part of my career RTFM and advising other to do the same. However, in this case I do not even have the foggiest idea what FM to begin reading.

So here is my scenario:
My LAMP server root access
Client logs in to website somehow and loads a webpage using modern browser.
A script, either Perl or PHP, who cares, running on the server regularly updates the SQL database on the server with new records.

I need the server to see that this record has been added and push the contents to the clients web browser via HTML.

Other factors:
Client side bandwidth is extremely expensive (wireless 4g/lte etc.) I had considered setting the client webpage to auto reload a CGI or something. However that will chew my precious data. Also even if I set it to refresh every two seconds that would bring me updates only after 2 seconds. I would like an instant update when the database adds a record. I don't want to wait 2-3 seconds for the browser to refresh.

Generally speaking I know how to pull the data out of the SQL database and format it into a html document using PHP or perl. The issue is I have no idea how to create that connection to that will allow the SERVER to update the page without some constant bandwidth eating exchange of data going on.

So, essentially I know something like this exists. I see it when I use a spread sheet in google drive that I am collaborating with another person on. I see their updates and the cells they are working on change color in real time.
Any suggestions about what languages or protocols could accomplish this would be appreciated. I will do the research on how to implement it if I at least know what to study.