What is Sharepoint ?

As defined by Wikipedia

Microsoft SharePoint is a Web application platform developed by Microsoft. First launched in 2001,[3] SharePoint has historically been associated with intranet, content management and document management, but recent versions have significantly broader capabilities.

As defined by Microsoft

Organizations use SharePoint to create websites. You can use it as a secure place to store, organize, share, and access information from almost any device. All you need is a web browser, such as Internet Explorer, Chrome, or Firefox.

Other definitions
At its most basic definition SharePoint is a web application from Microsoft that enables organizations to work more efficiently by letting users share documents, data and information. There are multiple SharePoint products for organizations to choose from, each offering a unique set of benefits.

In Simple terms
SharePoint is a:

• Document management server
• Web content management server
• Portal solution
• Search engine
• List-based repository
• Collaboration site
• Replacement for file shares
• etc etc...

...to summarize in one sentence what SharePoint is I would say: 
Sharepoint is Microsoft's Web OS.

Finally as explained by MSDN

The following is a selection of some of the most important things that SharePoint is:

• A portal server with delegated administration. SharePoint enables information workers (IW) who have no knowledge of website design or website administration to create, almost instantly, attractive and functioning websites. This relieves information technology (IT) departments from the burden of creating and administering the sites, and it empowers the IWs to create their own sites for teams, blogs, wikis, and other purposes.
• A groupware application kit. SharePoint provides a platform on which IWs can create collaboration solutions that include document libraries and workspaces, workflows, wikis, blogs, and team-oriented lists, such as Events, Announcements, and Tasks. Microsoft SharePoint Workspace (formerly Microsoft Office Groove 2007) provides an offline experience for these collaboration solutions.
• A workflow host. Business processes can be systematized and modeled with workflows that are triggered by associated events; for example, the addition of a document to a document library.
• A content management application. SharePoint Server Enterprise Content Management (ECM) features include document management, records management, and web content management.
• A Business Intelligence (BI) application kit. The Microsoft Business Connectivity Services (BCS) features of SharePoint enable data from non-SharePoint sources, such as a SAP installation or Oracle database, to be accessed (read/write) just as if it were an ordinary SharePoint list.
• The operating system of an intranet. SharePoint can provide for an intranet many of the functions that an operating system provides for a computer, including storing and copying files, hosting services, starting applications, and securing data. (This is not to imply that SharePoint can only be used on an intranet. SharePoint can also host extranet and Internet-facing solutions.)
• A host for services. SharePoint deployments make data available through a client object model, the REST-based Windows Communication Foundation (WCF) Data Services (formerly ADO.NET Data Services), and many out-of-the-box ASMX web services. In addition, the SharePoint Service Application Framework provides a platform that enables developers to build scalable middle-tier services that can provide data or processing resources to other SharePoint features.
• A data store. SharePoint stores data as multicolumn lists in a Microsoft SQL Server database. You can query the data by using LINQ and also using Collaborative Application Markup Language (CAML). The data can be mirrored, backed up, restored, and, depending on the edition of SQL Server being used, you may be able to take snapshots of the data store.
• A data and processing layer for multiple user interfaces (UIs). Besides its native UI of webpages (including special versions for mobile devices), which can contain ECMAScript (JavaScript, JScript), SharePoint also supports access from Microsoft Silverlight applications and the Microsoft SharePoint Workspace client application. With the SharePoint client object model, you can access SharePoint using Windows Presentation Foundation (WPF), Windows Forms, or any other managed code application
  
  Hope this helps...Happy Coding!!!!