A Widget is a small block of code that performs a specific function. You may add widgets in sidebars and other asides.
In order to embed your instagram feed you can use a service like Snapwidget.com - here is one sample, which will give you a basic idea. With Snapwidget you can create widgets for several SoMes, like Facebook, Instagram, Twitter etc.
- The present sample: Snapwidget
- An alternative: Lightwidget
- By thine own ingenium find better alternatives.
Around 2015 or so Instagram changed the API in order to stop malicious hacks.
- Mac Rumours (2015): Instagram Institutes API Changes That Will Kill Off Malicious Third-Party Apps
The files in the folder deprecated are pure web archeology - after the API changes, the files don't work any more.