Power BI is an self-service business intelligence offering from Microsoft. It is primarily aimed at business users to access corporate information (and even information outside of the organization) without (or with the least) involvement of IT. Users can build their own business intelligence solutions, share and collaborate with team members and finally publish this information.
From the mid 2000s, with the launch of SQL Server 2005, Microsoft had been striving to bring business intelligence to the masses. Business Intelligence at that time was mostly used by large enterprises and was quite a costly solution to put into place. So, when SQL Server 2005 came into being with a new and improved Analysis Services, sporting Unified Dimensional Model, all of a sudden even small organizations could implement BI.
Fast forward to the present, we have self-service BI and analytics running the show, and Microsoft is in the middle of the game once again with Power BI. If you would like to learn more about Power BI and what it offers, I have a curation on Curah! dedicated especially for this. The content of the curation will change as Power BI evolves, so go take a look: https://curah.microsoft.com/348325/what-is-power-bi.