LAMP is a common term for the software bundle of Linux, Apache, MySQL and PHP. All of these items are open source and free software. Using the LAMP software set (or "stack") to develop web sites, web services and components is hugely popular.
The success of LAMP exemplifies the success of the open source movement. All the LAMP software are free. All the components are mature and benefit from a large and committed user community which continues to develop, refine and improve each of the stack components. The components are reliable and have large support resources which help users learn and develop software using LAMP. Bugs are reported throughout the community and frequent software releases help improve the reliability of the products.
All the components of the LAMP stack are interchangeable. For example an alternative is LAPP (the Postgres database replaces MySQL) and another is LEMP (NginX - pronounced Engine X - a light-weight web server replaces Apache).