Microsoft SharePoint is a Server Product that leverages Web 2.0 Technology to assist the client in improving the way information workers work together today. The vision is to go away from local storage of information towards a centralized information hub helping the information workers by automation of reoccurring tasks, creation and sharing of common documents, terms and information as well as finding this and other information via search or help of colleagues by (a)-synchronous communication.
SharePoint history began in 2001 when Microsoft introduced a system that associated content and document management with web technologies for the first time.
The subsequent versions SharePoint 2003, MOSS 2007 (Microsoft Office SharePoint Server 2007) and SharePoint 2010 Server and the soon upcoming SharePoint 2013 have developed into a strong Server Product with the moste notable advantages of flexibility and integrational capabilities. The bandwidth of features and possibilities has grown SharePoint into a touchpoint with all other Microsoft Products and can so be the central component in the IT-Infrastructure of today and tomorrow.
Sites: The SharePoint platform fundamentally enables users to provision 'sites' (public or private) without a requirement for specialized knowledge. SharePoint is designed to become the central location for management of sites in an organization.
Communities: SharePoint aims to support the formation of communities within an organization - these communities may form around teams, projects, clients, geographic locations, etc. SharePoint also provides social features and social integration.
Content: SharePoint provides a central location to put content such as files, documents, or general information. This can be accessed and modified within a web browser or using a client application (typically Microsoft Office) via desktop or smartphone. SharePoint 2010 also provides a concurrent edit ability with Office 2010.
Content: SharePoint provides a range of search abilities, including in documents, in external content (such as network shares or public websites), and in user profiles.
Insights: SharePoint provides data integration, data crawling, and report design to enable business decision making. SharePoint can integrate with SQL Server Reporting Services to surface business intelligence.
Composites: SharePoint provides an application platform based on ASP.NET 3.5 allowing no-code development of complex business problems using SharePoint Designer. SharePoint also allows custom code to be developed using Microsoft Visual Studio 2010.
If it's still not clear what SharePoint can do for you, watch this video: