Sometimes called a 'Data Grid', Data Tables is a name for systems that present data to the User Interface in a robust way without unnecessary programming. "Unnecessary programming" is a complicated phrase. It's good to know the frameworks (e.g. jQuery), because they're powerful and quite often in demand. However, you should know how the underlying technology works, and sometimes that is both necessary and more in demand [1].
- https://datatables.net/index is a plugin for jQuery that I've used. It's probably the #1 solution in the category
- Steve Schwartz created DynaTable This is even cooler. Best of all, it's AGPL licensed, so it's completely free software, and will remain so.
- http://ajaxpatterns.org/Data_Grid is interesting, but fairly old (2010 last major edit), and doesn't even mention datatables
- http://lazymofo.wdschools.com/ actually offers a free (MIT licensed) PHP Data Grid
There are other solutions that create CRUD interfaces to databases, but they're either not worth mentioning, or I haven't fully researched it. There used to be a phpGrid that was free (GPL) software, but not now. phpgrid.org and phpgrid.com definitely are not