I'll give you a *very loose* **analogy** (emphasis is important here) that may help you understand the intuition. There's this technical drawing tool, called a [French curve][1], here's an example:

[![enter image description here][2]][2]

We were trained to use it in high school in a technical drawing class. These days, the same class is taught with CAD software, so you may not have encountered it. See, how to use them in [this video][3]. 


Here's a straight ruler:

[![enter image description here][4]][4]  
<sub>(source: [officeworks.com.au](https://images.officeworks.com.au/api/2/img/https://s3-ap-southeast-2.amazonaws.com/wc-prod-pim/JPEG_300x300/SM388590_studymate_wooden_ruler_30cm.jpg/resize?size=300&auth=MjA5OTcwODkwMg__))</sub>  


Can you draw a curved line with a straight ruler? Of course, you can! However, it's more work. Take a look at [this video][5] to appreciate the difference.

It's more efficient to use a French curve to draw curved lines than with a straight ruler. You'd have to make a lot of small lines to draft any smooth curve with the latter. 
[![enter image description here][6]][6]

[![enter image description here][7]][7]

It's not exactly the same with machine learning, but this analogy provides you with an intuition why nonlinear activation may work better in many cases: your problems are nonlinear, and having nonlinear pieces can be more efficient when combining them into a solution to nonlinear problems. 


  [1]: https://en.wikipedia.org/wiki/French_curve
  [2]: https://upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Krzywiki.jpg/130px-Krzywiki.jpg
  [3]: https://www.youtube.com/watch?v=wgATTmC0JSQ
  [4]: https://i.sstatic.net/qz1E3.jpg
  [5]: https://www.youtube.com/watch?t=2m58s&v=uulfOWzIe9o
  [6]: https://www.sewalongs.com/media/2011/08/using-a-French-curve-500x3331.jpg
  [7]: https://i.sstatic.net/pDJrB.jpg