While some people use Classical Dungeons & Dragons to refer to both the original D&D booklets from the mid-1970s and the various Basic, Expert, etc. Dungeons & Dragons boxed sets sold in the 1980s as a separate line from the Advanced Dungeons & Dragons game, this site uses the term to refer only to the 1980s boxed sets (and the Rules Cyclopedia published in the early 1990s) and the adventures and accessories designed for them.
While some players of Advanced Dungeons & Dragons looked down their noses at this "plain" Dungeons & Dragons because the "advanced" part of the name held snob appeal for them, Classical D&D was every bit as good a system as the first edition of AD&D (and arguably better than the second edition). It just made different design choices and was designed to be learned in stages with new rules added as characters advanced. According to reports from TSR employees, it sold almost as well as first edition AD&D.
There were two major editions of Classical D&D. The first consisted of two boxed sets: a Basic Set by Tom Moldvay and an Expert set by David Cook. This version is often refered to as B/X or Moldvay/Cook. The second edition was written by Frank Mentzer and consisted of five boxed sets: Basic, Expert, Companion, Masters, and Immortal. This version is often refered to as the BECMI edition or the Mentzer edition. The Rules Cyclopedia, edited by Aaron Allston, combined the rules material from the first four Mentzer boxed sets with some new material (and some new errata).