When you Share something on Facebook, Facebook will use the most recent information that its scraper has cached from your pages. If FB scraper has not yet crawled a page, then it will read your metadata and generate the content for the shared post at that time.
Usually it will prefer to see Open Graph meta tags.
A sample of og:metatags that can exist on a page, to describe its content for FB sharing:
<meta property="fb:admins" content="100000375458816">
<meta property="fb:app_id" content="633297421913264">
<meta property="og:url" content="http://www.mysite.com/about">
<meta property="og:title" content="My About Us Page Title">
<meta property="og:type" content="article">
<meta property="og:description" content="My about us Page Description">
<meta property="og:image" content="http://www.mysite.com/images/about-us.jpg">
If those do not exist, it will use the default meta tags of your website.
So make sure your pages meta have the desired content - this involves reviewing your global metadata and also the metadata of your individual pages (e.g. menu items metadata and article items). Finally after any changes it is suggested to have your Joomla's site cache cleared, in order to display the most up to date data.
Facebook scraper usually caches the content for 24 hours (if I can recall this right).
You can force facebook scraper to clear the cached information of your page with the Open Graph Debugger Tool.