With massive changes from SharePoint 2010 to SharePoint 2013, People picker also has changed! In its previous versions, SharePoint 2010 and SharePoint 2007, people picker is associated with an address book and check name icons, which are missing in SharePoint 2013!
While its still identical in some places of SharePoint 2013 (E.g. Setting up groups for the site: /_layouts/15/permsetup.aspx), These icons are missing in all other places. E.g In SharePoint list forms, Grant Permission pages, etc. But in SharePoint 2013 these places provides "Auto complete" feature in people picker to help us picking users.
Not very sure why Microsoft removed these nifty icons. Anyway, If you need the "Browse Icon" back in SharePoint list form people picker fields, simply create new custom list form using SharePoint designer, which brings browse button in people picker by default!
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