Where is this icon coming from?

We don't support physically replacing them... the best approach is to cutomize the widget it is in or use CSS/custom upload and override the existing style.   This is the best way if it is in fact a font image versus an actual image.

Can you please tell me from which widget this image(browser_2D00_dark.png)  is coming from. I looked towards Activity story Stream widget iam not able to find it.

This is not specifically related to the stream.

When a URL is shared within content on Community (in the stream or elsewhere), a preview of it is is attempted to be shown in place of the actual URL. The preview is scraped from the target URL using the Open Graph Protocol standard first (which defines metadata including, among other things, a preview image) and then falls back to simply looking for a title, description, and first image in the page. If no image can be found, the browser icon is shown.

So this should only occur for non-previewable URLs. Another cause could be if they can't be previewed, even if they do have images. Are the URLs not accessible to Community? If Community does not have access to request the URL from the server, it also would not be able to generate a preview and fall back to the default.

This functionality is called Web Previews in Community. The UI of a Web Preview is rendered via a UI component, which, like all UI components, can be overridden by the theme. 

Here is documentation containing the default implementation of the Web Preview UI component, which can be customized.

https://community.telligent.com/community/10/w/api-documentation/61992/webpreview-ui-component 

In this case, the UI component uses the $.telligent.evolution.preview module, and the preview module defines the default client-side template, as shown in its documentation here

https://community.telligent.com/community/10/w/api-documentation/61894/preview-javascript-api-module

I'd recommend customizing the theme to re-define the $.telligent.evolution.preview.template client template as you see fit.

Excellent. We'll have a look at this.

We looked at this but this is a huge undertaking for such a small mod. Is it possible to change the color of this image that fits with the default style? I cannot imagine this image passed the Style Council of Telligent because it is off-style with the rest of the platform. We modified the style but retained most of the original style. This image stands out in every aspect.

Or in in brutal dutch: It is really ugly

It is not possible to change the icon. The options are to use CSS to override or use JavaScript to redefine  $.telligent.evolution.preview.template. The latter option sounds complicated, but it's likely only about 10 lines of code in your theme.js.

UI components (the latter option) are specifically designed to be theme-overridable for these kinds of cases to ensure that no theme is stuck with any part of the platform's defaults.