There have been a lot of versions and revisions of D&D over the years. Amongst players of the earlier (or "classic") versions of the game, 'B/X' stands for play based around the Basic Set edited by Tom Moldvay, and the Expert Set edited by "Zeb" Cook, both published in 1981.
The 'B/X' edition of the game came after the "Holmes" boxed set,first published in 1977 and edited by J. Eric Holmes, and before the BECMI (Basic, Expert, Companion, Masters, Immortals) published in 1983 and later (and eventually compiled in the D&D Rules Cyclopedia published in the early '90s). They existed at the same time as Advanced Dungeons & Dragons, which had more, and more complex, rules.