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Unless a system is simple and intuitive to use, your investment may be wasted because users are not encouraged add content and explore its features. For this reason, each version of SharePoint has made significant improvements to usability and SharePoint 2013 is no exception. Document content is readily accessible throughout SharePoint sites, Office applications are thoroughly and intuitively integrated, and comments and tags can be widely used.

Office Web Applications
Office Web Applications were available in SharePoint 2010 and enabled users to open and edit Office documents in a browser. In SharePoint 2013, Office Web Applications are more closely integrated in the user interface. For example, in a document library, the context menu for a document includes a preview generated by Office Web Applications.
Apps for Office (formerly Office Agave)
Apps for Office are custom user interface elements that users can add to Office applications such as Word, Excel, and PowerPoint to extend functionality. They are built using web technologies such as HTML5 and JavaScript so they work seamlessly in SharePoint sites viewed in the browser.
Social Networking Support
Social features have been redesigned in SharePoint 2013 and integrated throughout the product to maximize user communication. The My Site has been extended with a micro feed of sites, documents, people, and tags so you can stay informed on all relevant topics. There is also a new Community site template.
Translation Services
Documents in Office formats can be automatically translated by this service
Application. Translation Services makes use of the Bing Translation Service available in the cloud.
Work Management Services
Users may have to check multiple locations for tasks to complete in their workday. By using the Work Management Service application, you can integrate task lists stored in SharePoint, Exchange, and Project Server. The consolidated list is viewable in My Site and Outlook so users can more easily plan their time.

Core Capabilities

Request Management
Administrators can use the Request Management feature to distribute
Incoming requests across Web Front-End servers in the SharePoint farm. For example, they can use static weights to route more requests to a new, high specification server and thus take load off an older, slower server. You could also route all requests from a particular browser, such as IE9, through a specific server or deny requests from certain IP address ranges.
Shredded Storage
When users make changes to documents, SharePoint 2013 can apply those
changes to the document in the content database without a full refresh of the whole document. If only a single change has been made to a large document, this can enormously reduce the quantity of data sent over the network and, if versioning is used, the volume of the content database.
Enterprise Content Management
Many improvements have been made to ECM especially in the field of eDiscovery, which is the process of locating all document records that relate to a specific subject or legal case. You can also use Team Folders to consolidate content stored in SharePoint and Exchange.
Web Content Management
In SharePoint 2013, the structure and navigation of a WCM site is defined by managed metadata terms. This approach is highly flexible and enables administrators to reorganize their entire Web site without moving any content.
Search
In SharePoint 2013 there is a single Search engine that combines the best features of the SharePoint and FAST search engines in SharePoint 2010. New configuration objects, such as Query Rules and Result Types allow administrators to customize result sets to an unprecedented level.
Client Object Model(CSOM)
The CSOM existed in SharePoint 2010 but has been greatly extended in SharePoint 2013 to enable access to almost all SharePoint 2013 functionality from JavaScript and other client-side code.

Life Cycle Management
In SharePoint 2013 there is a new custom component called the apps for SharePoint. This is the recommended way for developers and third parties to create new functionality and user interface components. However the SharePoint 2013 Apps infrastructure also benefits SharePoint administrators by making it easier to manage the life cycle of custom applications.

Sharepoint Market Place
This global marketplace for apps for SharePoint is a single repository of custom components, available to all SharePoint customers. Administrators can enable users to purchase apps, on behalf of the company from the marketplace, or restrict that right to a small number of budget holders. Once purchased, an app becomes available to all users in the SharePoint farm.
Corporate App Catalog
This catalog is a private repository of apps within the SharePoint farm and controlled by farm administrators. Users can choose to install these apps in any SharePoint site in the organization.
Remove Apps
Apps for SharePoint is contained entirely within a sub-site of the SharePoint site in which it is used. Therefore, whennt Market Place
This global marketplace for apps for SharePoint is a single repository of custom components, available to all SharePoint customers. Administrators can enable users to purchase apps, on behalf of the company from the marketplace, or restrict that right to a small number of budget holders. Once purchased, an app becomes available to all users in the SharePoin a user or administrator removes the app, the sub-site is removed cleanly and no objects are retained in the parent site or elsewhere. This clean removal aids app management.
Multi Tenant Farms
In a multi-tenant SharePoint farm, there is a one Corporate App Catalog for each tenant organization. This ensures that both tenants must pay for their app usage and that removals do not impact other tenants.

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SharePoint 2013 Features - TechNet Articles - United States (English) - TechNet Wiki

SharePoint 2013 Features