SharePoint 2013 is a massive and complex product. Not only is SharePoint itself complicated but it also relies on a whole series of other technologies to make the magic happen.
The SharePoint 2013 technology stack consists of
Computer servers: At the root of any software system is a physical device called a server. A server is no different than your laptop, desktop, or even phone. They all use physical computer chips to make things happen in the digital world. A SharePoint server is just designed specifically for heavy-duty enterprise-type software.
Operating systems: A physical computer isn't much more than a paperweight without software to make it function. The software designed to make computers do stuff is called an operating system. In the Microsoft world, the operating system designed for servers is called, aptly enough, Windows Server.
Databases: A database is installed onto the operating system and is specifically designed and optimized to store and manipulate data. The Microsoft database product is called SQL Server. SharePoint takes advantage of the advanced capabilities of SQL Server to provide the features users need.
Web servers: SharePoint is software that you interact with using your web browser. A special software product called a web server is the engine that delivers web pages to your web browser. The Microsoft web server is called Internet Information Services (IIS).
You have a few different options when choosing SharePoint 2013:
SharePoint Foundation 2013: Basic collaboration using team sites, blogs, and apps
SharePoint Server 2013, Standard license: Intranet, portals, extranets, search, and My Site social network
SharePoint Server 2013, Enterprise license: Advanced scenarios for business intelligence, application integration, and Office 2013 services
SharePoint Online: The cloud-based version of SharePoint 2013, offered as a standalone product or bundled with Office 365, includes a number of different package options that are a mix of the SharePoint Foundation and SharePoint Server features.