Your comments

+1

Oftentimes the branch name is not informative enough, we have to use more or less ugly workarounds. This would be very useful feature. It's strange that github does not support it (yet).

How this could be done...

The content of the description is plain UTF-8 text. Markup (or markdown) probably should not be supported.

Except that URLs and references to tickets in jira etc prepended by # or enclosed in [ ] may be rendered as clickable links. 

The branch description should be visible in the work tree view for the active branch (or open by an icon on the main toolbar)

The create/edit description command can be added to Branch menu and in the branches list on the left side, context menu; open a simple edit/text box.


"Display" action can be also added in the tree view,  context/right click menu on commits that are branch heads and  branches list on the left side.