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 Administrator by the Module Manager (help screen).
Module positions are placeholders in a template. They identify positions within the template and tell the Joomla! application where to place output from modules assigned to a particular position. The template designer has complete control over module positions, creating variations between templates and the respective Joomla! default positions assigned to modules in the installation sample data.
For example, the module position Left could be defined to be on the left side of the template to display a site navigation menu. So if a module is assigned the Left position, it will be displayed wherever the designer puts that Left module position - not necessarily the left side of the page.
Joomla 1.6 and newer will only show the template positions with ?tp=1 or &tp=1 if the Preview Module Positions mode in the Template Manager has been enabled: Extensions > Template Manager > Options (upper right corner) > (templates tab) Preview Module Positions: Enabled.
For more developer information, see Module Development.