The segmented control is used to group like buttons together.
The control is native to Mac OS X [1] and seems to be native to GTK+ 3 as well [2], being used for e.g. navigation buttons in Nautilus [3]. For Qt, see http://stackoverflow.com/questions/3610234/create-capsule-style-toolbar-controls-in-qt . Windows don't seem to offer a native control, but Microsoft still uses it in e.g. Office 2007 [4].

This kind of control is important for visually grouping related commands [3][5]
as well as separating tabs from content area when appropriate [6], and is key to furthering LibreOffice's UX.

[1] https://developer.apple.com/library/mac/documentation/userexperience/conceptual/applehiguidelines/Controls/Controls.html
[2] I'm not exactly sure what GTK+ 3 offers. Buttons that are part of the "inline-toolbar" class (http://stackoverflow.com/questions/9855671/python-gtk3-treeview-buttons) display this way, as does GtkStackSwitcher.
[3] https://upload.wikimedia.org/wikipedia/commons/2/28/Nautilus-3.10.0.png
[4] http://3.bp.blogspot.com/_-mvkf0zdGLY/TVAqGbwwJzI/AAAAAAAAAAQ/iBpm-acRL0E/s1600/Word2007.png
[5] http://fc06.deviantart.net/fs71/f/2013/030/2/3/writer_concept_by_spiceofdesign-d5t9wcs.png
[6] Such as in https://wiki.documentfoundation.org/images/5/5a/Impress-tabs.png from the UX guidelines -- https://wiki.documentfoundation.org/Design/Guidelines