Handlebars is a simple templating language used by Foundry VTT to structure HTML based on JS object data stored by systems, modules, and FVTT itself. You can find out more about Handlebars by clicking here.
You can find out more about jQuery here.
PixiJS is a powerful HTML5 WebGL library which powers FoundryVTT's canvas, it is extremely robust and provides FVTT with its lighting renderer and many other Scene features. Numerous modules leverage PixiJS to extend Foundry VTT in profound ways, adding lighting, filters, and even animated effects.
You can find out more about PixiJS here.
You can find out more about Greensock here.