This is a way of graphically depicting the linear and harmonic relationships that underlie a musical surface.
A stemmed note (resembling a quarter note) is used to mark a musical event (a chord, phrase, period, or section) that is of relatively great tonal significance.
An unstemmed note (resembling a blackenedwhole note) is used to mark a musical event (a chord, phrase, or section) that is of relatively less tonal significance.
Different stem lengths may be used to indicate events of varying degrees of structural importance.
Slurs are used to connect
(1) unstemmed noteheads to the stemmed noteheads on which they are conceptually dependent
(2) stemmed noteheads to one another, to show relatively large-scale connections.
Beams may be used to connect stemmed noteheads that form a large-scale progression within a composition.
Stema and slur notation is dervied from the graphic analyses of Heinrich Schenker (1868-1935). His final text, Free Composition, is an explanation of his analytical and interpretive methods, which rely heavily on species counterpoint as a model of how tonal music works. His notion of structural levels is perhaps the most important theoretical concept for music theory since Rameau formulated the concept of chord roots in the 18th century.
Heinrich Schenker, Free Composition (trans. by Ernst Oster; Schirmer Books, 1979)
Cadwallader and Gagné, Analysis of Tonal Music: A Schenkerian Approach (Oxford University Press, 1998)
Robert Gauldin, Harmonic Practice in Tonal Music (W. W. Norton, 1997) -- see especially pp. 103-111.