Barbershop quartets sing without accompanying instruments -- or a cappella. They sing four-part chords. Typically, the lead sings the melody, the tenor harmonizes above the melody, the bass harmonizes with the lowest notes and the baritone fills out the chord, usually between the lead and the bass. In both men's and women's barbershop, quartet parts are lead, tenor, bass and baritone.
In a men's vocal quartet, the parts are typically first tenor, second tenor, baritone and bass. The second tenor part is sometimes called the lead.
In a women's quartet, the parts are typically divided into soprano, alto, tenor and contralto. The majority of quartet music is written with the soprano singing the melody and the other parts harmonizing.
Mixed quartets are typically two men and two women. When divided this way, the parts are soprano, alto, tenor and bass.