Scale, all correct. But I am trying to rephrase to better insert it into the historical discussion.
The concept of "absolute music" is a ROMANTIC concept. The Romantics (writers, poets, and philosophers, not musicians) developed a series of aesthetics of the ineffable, of theories for which the only language of the absolute is music. A consequence of this aesthetic of music as the supreme language is the denigration of every musical form that 1) involves the use of the voice or, more precisely, a linguistic text 2) involves the use of music in a functional role 3) is, in a certain sense, the musical setting of a text or a situation. Absolute music, therefore, is instrumental music without functional ties that communicates, if possible, musical (non-referential) meanings.
Functional music, as Scalaquaranta said, is that which "serves" something or serves as a background to something. And functional music includes dance music, liturgical and sacred music, and film/stage music. In Romanticism, the number of sacred compositions decreases drastically, also because it is taken for granted that all music is sacred. But it is worth emphasizing again how the concept of absolute music was developed mainly by Romantic theorists, not so much by composers. Although in words almost everyone spoke ill of opera and no one had "religious" commissions, in reality many Romantics wrote operas and just as many wrote sacred compositions. Not to mention, then, the various choral, Lied-style, didactic compositions, etc., etc.
The situation regarding referential music, then, truly gives an idea of the distance between theory and practice. Hanslick was the great proponent of the idea that music should communicate only musical meanings. That is, it's not beautiful when Vivaldi makes the violins trill as if they were finches, but it is beautiful when Brahms communicates nothing precise, only "musical beauty." In Hanslick's trash can, practically all symphonic poems, many overtures, and many characteristic pieces based on texts, paintings, or scenes should be thrown. Absolute music takes pure chamber forms (the quartet, which is practically the only 19th-century chamber form) and classical orchestral forms (symphony and concerto) as models. There is room for other things, but very little else...