The word Balearic in its most most simple terms means "of or having to do with the Balearic Islands" which are a group of small islands in the Western Mediterranean near the coast of Spain.
More specifically however, the term Balearic (or "Balearic Beat") has come to mean a genre of music which became popular on the islands of the same name, specifically the Balearic Island of Ibiza.
The Balearic genre is broad and almost means "eclectic" more than any specific style of sound. Generally, it tends towards sunny, melodic, "feel-good" electronic music, as it's birthplace was on the warm sunny beaches of the islands. This may encompass atmospheric house, downtempo, chillout, nu-disco, latin,soul, dub, and re-edits.
As mentioned before, the genre is about being eclectic, so a Balearic Beat DJ will often flow through many different sounds inside a single set. In fact, "Balearic" might be better thought of as a style of DJ'ing rather than a style of music. Still, the flavor always comes back to that sunny island feel and often incorporates smooth soul sounds, acoustic strings and guitar, dreamy vocals, and tempos under 120 BPM.
I was loving the Balearic set that DJ was playing last night during sunset!