What is the attribute property="og:title" inside meta tag?
og:title is one of the open graph meta tags. og:... properties define objects in a social graph. They are used for example by Facebook.
og:title stands for the title of your object as it should appear within the graph (see here for more http://ogp.me/ )
The property in meta tags allows you to specify values to property fields which come from a property library. The property library (RDFa format) is specified in the head tag.
For example, to use that code you would have to have something like this in your <head tag. <head xmlns:og="http://example.org/"> and inside the http://example.org/ there would be a specification for title (og:title).
The tag from your example was almost definitely from the Open Graph Protocol, the purpose is to specify structured information about your website for the use of Facebook (and possibly other search engines).
A degree of control is possible over how information travels from a third-party website to Facebook when a page is shared (or liked, etc.). In order to make this possible, information is sent via Open Graph meta tags in the <head> part of the website’s code.