Secular music in the Middle Ages included love songs, political satire, dances, and dramatical works, but also moral subjects, even religious but just not for church use. Non-liturgical pieces such as love songs to the Virgin Mary would be considered secular. Most secular music was syllabic and had a narrow range. Rhythms are largely unknown, and probably slight improvisation, at least for decoration, was common.
Naturally there is little evidence of secular music and musicians. The 10th century had its jongleurs and minstrels, travelling vocal and instrumental performers relying on an oral tradition and playing mostly music by others, of low social status parallel to carnival workers today. The 12th and 13th centuries saw the Goliards, scholar poets or gypsies singing in Latin of wine, women, and politics. (See Orff's Carmina Burana from the 1930s.)
In southern France, singing in Provençal, the troubadours composed their own strophic songs of love, politics, pastorales, dance songs, etc. Trouveres in northern France, minnesingers in Germany in the 12th to 14th centuries (minne = love), and their counterparts in Spain with cantigas, similarly provided secular music. Famous surviving music includes "Jeu de Robin et de Marion" by Adam de la Halle (c. 1237-1287) from a play descended from the pastorale tradition, Walther von der Vogelweide's "Palastinalied," and the ravishing "A chantar" by Beatriz de Dia (died c. 1212).
Bonds, Mark Evan. A History of Music in Western Culture. Upper Saddle River, NJ: Prentice Hall, 2003.
Crocker, Richard. A History of Musical Style. NY: McGraw-Hill Inc., 1966.