that is publicly available (i.e. it can't be inside your facebook account, for example) ... into a DU message ... and it will show up here when you post your message.
The URL does need to actually end with .jpg .png or .gif (and maybe some others are supported) so not every image you come across on the internet can be linked in this way because the site it's on isn't publicly exposing the URL that leads directly to the picture (and hence you'll have no means of linking to it).
It's really not that arcane.
An easy way to put images into a DU message is to get an IMGUR account. Then you just upload image file to your imgur account, then copy the URL from imgur that points to the photo you uploaded and put it in your message. Here's a screen shot I just took and uploaded to imgur and got the URL for ...
https://i.imgur.com/6HvA4yJl .png
Directly below this paragraph is the same link as the one above, but without the extra space. DU knows that this link is to a photo file (because it ends with .png) and presents the picture inline.