Bill was from Kentucky, which is the “bluegrass” state (theoretically the grass there is so green it’s blue). Monroe’s music draws from a number of musical traditions: the Scotch-Irish ballad tradition of the Appalachian mountains, the bluesy sound of African American musicians who interacted with Bill, and the roots of country music via the Carter Family.
A lot of traditional bluegrass is Carter Family on speed. Bluegrass’s unique sound derives from its instrumentation: guitar, banjo, bass, fiddle with mandolin and dobro as optional additions (although Monroe was a mandolin player, so it was mandatory in his band).
Each instrument has a distinctive role to play in bluegrass. The bass is the heart beat. The mandolin chops (plays a short note) on the off beat where the bass is silent. The guitar combines the rhythms of the bass and mandolin (beat and offbeat) but adds special runs between the chords and as ornamentation. The banjo is picked with three fingers, thumb, index, and middle, which have special picks on them.
Earl Scruggs, who played with Bill Monroe in the early days, popularized this style of banjo picking and created many well-known tunes in this style, such as Foggy Mountain Breakdown. Rhythmically, the banjo roll the three fingers play in succession, playing melody and harmony notes in succession. The fiddle is played in a bluesy style, with slides and syncopations.
In general, every bluegrass player gets an opportunity to take a break or solo while the other musicians play accompanying parts. If the piece is an instrumental, each break will be performed in turn by different musicians.
For example, in Foggy Mountain Breakdown as performed by Flatt and Scruggs, the piece begins with Earl playing the famous melody on the banjo. Paul Warren, their fiddle player then takes a turn on the fiddle, playing the melody in a fiddle style so that the essential notes are hit but the overall sound is different from the banjo version. If the piece is a song, one instrumentalist might kick it off by playing a break. The singer sings a verse and a chorus and then another instrumentalist will play a break.
If you are interested in traditional bluegrass, look for names such as Bill Monroe, Flatt and Scruggs, Ralph Stanley (who was featured in the film, O Brother Where Art Thou), Don Reno, Country Gentlemen, and Jimmy Martin. There are many new and wonderful bluegrass bands that derive their styles from these bluegrass pioneers.