Manual:$wgAllowExternalImages

Whether to allow inline images hosted on external websites, sometimes called hotlinking.

Details
When set to true, users can bring in an inline image from an external URL. They do this simply by sticking the full URL into the wiki text (without any other surrounding markup) That is the direct URL to an image resource on another website.

When set to false, the full URL appears as a text link to the image.

Example:
Using wikitext:  http://en.wikipedia.org/upload/b/bc/Wiki.png 

Result: http://en.wikipedia.org/upload/b/bc/Wiki.png

Why allow external images?
Users who know how to get the direct URL of an image, may find this a very useful way of adding illustrations to wiki articles, using image resources available elsewhere on the web.

Without this feature, users are forced to upload any image which they want to embed directly on an article. Upload is (in many ways) more fiddly and time consuming. It also uses disk space and bandwidth on the wiki webserver of course. There are many legitmate uses of inline images.

Why disallow external images?
Inline external images are disallowed on across may wikimedia projects, and MediaWiki has AllowExternalImages set to false by default since version 1.6.9 Reasons for this.... To prevent (or reduce the impact of) certain types of vandalism.

To prevent "bandwidth theft" from other sites