A user level on a Joomla site with access permissions to the back-end (via a separate log in) and some front-end privileges. Think of Manager users as Publishers, with Back-end access.

In Joomla! a Category is a collection of Articles. In Joomla! a website might have Categories called "Animals" and "Plants". Within the "Animals" Category, the website might have Sub Categories such as "Birds" and "Mammals". Within the "Birds" Category, the website might have Articles such as "Parrots" and "Sparrows".

The example above could be expanded even more with specific articles on different species of Parrots and Sparrows. Start with using an "Animal" Top Category. Placing the Sub Categories "Birds" and "Mammals" are under the Animal category, and then a "Parrots" and "Sparrows" Sub Category under the "Birds" Sub Category as shown.

Animals
Birds
Parrots
Sparrows
Mammals

Now you can create multiple articles in the Parrot and Sparrow Categories.

Categories are maintained using the Category Manager which can be reached in the Administrator (Back-end) by clicking on the Content menu, then the Category Manager menu item.

The database table prefix is a string (a few characters long) prepended to the name of Joomla!'s tables. Using a prefix enables you to run multiple installations of Joomla! using a single database.

The database table prefix can be set during installation. Changing it later is possible, but requires access to the database through a non-Joomla medium or a Joomla Extension such as Akeeba Admin Tools and will cause some downtime.

Extension developers need to use the string #__ to represent the prefix. This will be replaced by the real prefix during runtime by Joomla.

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