A component is a kind of Joomla! extension. Components are the main functional units of Joomla!; they can be seen as mini-applications. An easy analogy would be that Joomla! is the operating system and the components are desktop applications. They are usually displayed in the center of the main content area of a template (depending on the template).

Most components have two main parts: an administrator part and a site part. The site part is what is used to render pages when being called during normal site operation. The administrator part provides an interface to configure and manage different aspects of the component and is accessible through the Joomla! administrator application.

Joomla! comes with a number of core components, like the content management system, contact forms and Web Links.

Reference: http://docs.joomla.org/Glossary

The visible graphical interface features of an application are sometimes referred to as chrome. See Applying custom module chrome for information about how to modify the look of modules (in other words, the module "chrome").

Reference: http://docs.joomla.org/Glossary

Modules are lightweight and flexible extensions used for page rendering. These modules are often “boxes” arranged around a component on a typical page. A well-known example is the login module. Modules are assigned per menu item, so you can decide to show or hide (for example) the login module depending on which page (menu item) the user is currently on. Some modules are linked to components: the “latest news” module, for example, links to the content component (com_content) and displays links to the newest content items. However, modules do not need to be linked to components; they don't even need to be linked to anything and can be just static HTML or text.

Modules are managed in the Joomla! Administrator view by the Module Manager.

Joomla default modules:

• Archived Articles?
• Articles – Newsflash
• Articles – Related Articles
• Articles – Categories
• Articles Category
• Banners?
• Breadcrumbs
• Custom HTML
• Random Image
• Search?
• Statistics
• Syndication Feeds
• Feed Display
• Footer?
• Language Switcher
• Latest News
• Latest Users
• Login?
• Menu?
• Most Read Content
• Weblinks
• Who’s Online
• Wrapper

Reference: http://docs.joomla.org/Glossary

Joomla makes extensive use of the Model-View-Controller design pattern. A standard OOP design pattern that separates different logical functions into different classes to improve the maintainability of the software.

When Joomla is started to process a request from a user, such as a GET for a particular page, or a POST containing form data, one of the first things that Joomla does is to analyse the URL to determine which component will be responsible for processing the request, and hand control over to that component.

If the component has been designed according to the MVC pattern, it will pass control to the controller. The controller is responsible for analysing the request and determining which model(s) will be needed to satisfy the request, and which view should be used to return the results back to the user.

The model encapsulates the data used by the component. In most cases this data will come from a database, either the Joomla database, or some external database, but it is also possible for the model to obtain data from other sources, such as via a web services API running on another server. The model is also responsible for updating the database where appropriate. The purpose of the model is to isolate the controller and view from the details of how data is obtained or amended.

The view is responsible for generating the output that gets sent to the browser by the component. It calls on the model for any information it needs and formats it appropriately. For example, a list of data items pulled from the model could be wrapped into an HTML table by the view.

Since Joomla is designed to be highly modular, the output from the component is generally only part of the complete web page that the user will ultimately see. Once the view has generated the output the component hands control back to the Joomla framework which then loads and executes the template. The template combines the output from the component, and any modules that are active on the current page, so that it can be delivered to the browser as a single page.

To provide additional power and flexibility to web designers, who may only be concerned with creating new designs rather than manipulating the underlying code, Joomla splits the traditional view into a separate view and layout. The view pulls data from the model, as in a traditional MVC pattern, but then simply makes that data available to the layout, which is responsible for formatting the data for presentation to the user. The advantage of having this split is that the Joomla template system provides a simple mechanism for layouts to be overridden in the template. These layout overrides (often called "template overrides" because they form part of the template, although actually it is the layout that is being overridden) are bundled with the template and give the template designer complete control over all the output from the Joomla core and any installed third-party extensions that comply with the MVC design pattern.

Reference: http://docs.joomla.org/Glossary