YouTube is a very popular video website. While this may be a good solution for public videos, it’s probably not a good solution for publishing more ‘trusted’ videos – e.g. in an business/enterprise scenario. Part of Office is Office 365 Video. This is a solution where Sharepoint is the means to store, manage and publish you company videos and Azure Media Services is the incorporated solution to make sure the videos can be played on any device in the best quality.
This video gives a good business overview of what Office 365 Video is about:
This video shows what the technical solution behind Office 365 Video is:
More information can be found in this elaborate blogpost on Office 365 Video, including a FAQ.