LAMP stands for Linux, Apache, MySQL, PHP and refers to the "technology stack" that's used by the most popular web applications such as Wordpress, Drupal, Joomla!, MediaWiki and GNU social to name a few.
We normally use Debian on our servers, but Ubuntu is also used on some too. On our desktops and notebooks we use Linux Mint. Ubuntu and Linux Mint are both based on Debian, so the instructions for installations and configurations apply to all of three without any changes.
Nginx (pronounced engine x) is one of the preferred services that acts as a web-server, without a web-server the browser wouldn't get any response to its requests for my webpages.
A web-server's job is to listen for requests from browsers and deliver the page they ask for.
To see if Nginx is installed and running on my local machine I can access it on my browser by typing in the domain name localhost or the IP for it which is 127.0.0.1. If I go to either of those in my browser then I'll see if my computer has a site running on it.
I can stop and start nginx by typing in the following shell command
service nginx stop service nginx start
MySQL is a free open source database server, but a few years back it was bought out by Oracle. While it's still open source, the main developers didn't like the direction Oracle were taking it in, so they split off to make their own version called MariaDB which is the database server we use at Organic Design and recommend for projects we're setting up for others.