LAMP is an acronym for Linux, Apache, MySQL, and Php. These technologies are a common choice for running web servers.
Let us break this down a bit.
Linux is the operating system. For desktop and laptop personal computers your choices of operating system include Windows, Mac (OSX), or Linux. For servers your choices are either Windows or Linux. There are a few important points to consider:
Apache is the web server software. Nginx (pronounced like Engine-X) is another common web server, Although a typical LAMP stack could be running either Nginx or Apache, it is more accurate to refer to an Nginx setup as a LEMP stack (where the E is for Nginx).
MySQL is the database. The database allows your website to store information. MariaDB is another common database that is similar to MySQL. MariaDB is often used in instead of MySQL for LAMP servers.
PHP is the server-side scripting language. Server-side just means that the code is processed on the server before the web page is displayed to the end user. An example is logging into a website. When the user enters their username and password and clicks the login button their credentials are sent to the web server. PHP code will handle the actual authentication. The PHP code will attempt to retrieve the user's information from the database and verify that the given password matches the password that is stored in the database. All of this password verification logic happens on the web server before the user is "logged in" and sent to their user dashboard screen.
In other words, server-side code is processed on the company servers, client-side code is processed on your device.