Through-composed means either music that is completely non-repetitive, music that is not interrupted by dialogue, or music that is composed in linear order.
In music theory about musical form, the term through-composed means that the music is relatively continuous, non-sectional, and/or non-repetitive. A song is said to be through-composed if it has different music for each stanza of the lyrics. This is in contrast to strophic form, in which each stanza is set to the same music. Sometimes the German durchkomponiert is used to indicate the same concept.
In general usage, a 'through-composed' work is one based on run-on movements without internal repetitions. (The distinction is especially characteristic of the literature of the art-song, where such works are contrasted with strophic settings.)-- Webster (2004), 
Many examples of this form can be found in Schubert's "Lieder", where the words of a poem are set to music and each line is different, for example, in his Lied "Der Erlkönig" ("The Erlking"), in which the setting proceeds to a different musical arrangement for each new stanza and whenever the piece comes to each character, the character portrays its own voice register and tonality. Another example is Haydn's 'Farewell Symphony'.
A good deal of Captain Beefheart's oeuvre is through-composed. No section of Ary Barroso's 1939 samba "Brazil" repeats; however, a second set of lyrics in Portuguese allows the melody to be sung through twice.
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The term through-composed is also applied to opera and musical theater to indicate a work that consists of an uninterrupted stream of music from beginning to end, as in the operas of Monteverdi and Wagner, as opposed to having a collection of songs interrupted by recitative pieces and dialogue, as in the operas of Mozart. Examples of the modern trend towards through-composed works in musical theater include the works of Andrew Lloyd Webber and Claude-Michel Schönberg. In musical theater, works with no spoken dialogue, such as Les Misérables are usually referred to by the term "through-sung".