As an illustration, I have used the picture from the Wikipedia article "Harmonic series (mathematics)" which is at this URL: https://i.stack.imgur.com/Zxtnn.png
Basic information about the syntax for images is explained in the editing help. In this context, having a look at the part concerning links might be useful, too. (Very briefly, one could say that the syntax for images and links is a bit similar - but the images contain an additional exclamation mark.)
If you only add "the inner part"
![description], this creates an image. (Using the image in the link
 and the text "description" as alt-text. Of course, it is better to choose something more descriptive - the text "description" is just for illustration purposes.)
You can obtain exactly the same using
![description](https://i.stack.imgur.com/Zxtnn.png) if you prefer. Notice that this creates image which isn't a link - nothing happens after clicking on the image:
The way images are entered through the editor, image becomes a link. Which is basically the same thing as what you would get from
[link](https://i.stack.imgur.com/Zxtnn.png): link or link. (The help center calls these two styles of linking "a reference-style link" and "an inline link".) But now, instead of "clickable text" with a link to the given URL, you can obtain an image which links to the given URL:
In some situations you might consider preferable to make a picture linking to a different URL. (But I suppose this won't happen too often.) A possible syntax could be:
[![description](https://i.stack.imgur.com/Zxtnn.png)](https://en.wikipedia.org/wiki/Harmonic_series_(mathematics)). Now by clicking on the picture you go to the Wikipedia article:
Alternative, you could use a "reference-style" link instead of an inline link shown in the above example. One example of such usage is in this answer - where a screenshot of a chat message is actually a link to that message.