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][1]
, this creates an image. (Using the image in the link [1]
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 
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][1]
or [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: [![description][1]][1]
.

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: [](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.