LAMP is an acronym for the Open-Source software applications Linux, Apache, MySQL and PHP - probably the most common website "stack" platform on the Web. If you are a serious blogger or operate a website, it's worthwhile to be familiar with them.
The Linux operating system was developed by Linus Torvalds in 1991. It's roots can be found in the Unix operating system, and while not used on desktop computers as much as Microsoft Windows, it does have an active community and is popular on servers. Linux isn't a complete operating system - it's just a kernel. Linux distributions take the Linux kernel and combine it with other free software to create complete packages. There are many different Linux distributions out there such as Ubuntu, Centos, Fedora, Debian, Red Hat and more.
This Open-Source software application is technically the primary software 'web server'. It handles the chores of HTML GET requests, and opens and closes processes all day long. Think of it as the intermediary between the web-browser (e.g. Firefox, Internet Explorer, Safari, etc.) and your actual static and dynamic web files residing on the physical server.
The MySQL database server, is simply tables of data made available to multiple users simultaneously. It is a relational database that uses a Structured Query Language to add/edit/delete data.
PHP or "PHP: Hypertext Preprocessor" is the scripting language - or glue - that holds the pieces together. It runs as a process in Apache and it communicates directly with the MySQL server. It dynamically builds the HTML files that a browser renders.
These four Open-Source applications, commonly referred to as the LAMP stack, form a powerful and inexpensive alternative to proprietary website solutions. Nearly all hosting providers use a variation of the LAMP stack, whether it be shared hosting or a dedicated server.
Many web developers use a version of the LAMP stack on their own computers; MAMP (Mac, Apache, MySQL, PHP) and WAMP (Windows, Apache, MySQL, PHP). This allows the developer to build a website locally, and is useful for keeping a duplicate of a site as a backup, or for testing/staging new features.
Once you have the stack running, you can install a CMS (Drupal, WordPress, Joomla, etc.) or shopping-cart application (Magento) - those are the two most common uses, but there are others.