Multitasking

Presumably your iPad is running iPadOS15.

Unlike iPadOS14 and earlier versions, multi-tasking cannot now be disabled from settings. Multi-tasking has received a significant overhaul, both simplifying its use and introducing new controls.

Key to accessing and controlling multi-tasking is the small “three-dot” button that is found at the top-centre edge of the screen.

More information about using multi-tasking can be found in this support page:

Use multitasking on your iPad - Apple Support

The iPad User Guide is also a rich source of information about using iPad and its many features. The Guide is available both online using a web browser (such as Safari), or as an Apple Books download:

iPad User Guide - Apple Support

https://books.apple.com/book/id1567104892

Unlike iPadOS14 and earlier versions, multi-tasking cannot be disabled.

The “Shelf”, to which you make reference, is a new feature of the revised iPadOS multitasking environment. 

iPadOS permits you to have multiple “instances” of the same App - each instance being self contained. The shelf, when triggered, shows a thumbnail of each running instance of an App. 

For example, if you have three running instances of Safari, each with its own set of open tabs, you will see three thumbnails corresponding to each running instance of Safari - plus a button to open a new instance of Safari. Simply tapping a thumbnail will switch directly to that running instance of Safari. Each App has its own corresponding shelf.

This article from Appleinsider has a useful explanation of this new feature along with many of the updates to multitasking:

https://appleinsider.com/articles/21/08/12/how-to-master-multitasking-on-ipad-and-ipad-pro-in-ipados-15

The iPad User Guide is also a rich source of frequently overlooked information. The Guide is available both online using a web browser (such as Safari), or as an Apple Books download:

iPad User Guide - Apple Support

https://books.apple.com/book/id1567104892

You should note that the shelf is an integral component of the multitasking User Interface. It cannot be disabled.