Rhythm indicates the way musical patterns occur in time, moment by moment, as we hear them. At the macro level, tempo describes the pace of the music as a whole, while meter describes how the beats are grouped into measures consisting of stronger and weaker beats. A grouping of three beats lends a waltz feel, for example, while groupings of two or four drive the music forward. At the micro level of individual notes, accent and syncopation describe how each note meshes with the tempo and meter.
In "A Creative Approach to Music Fundamentals," William Duckworth calls melody "the horizontal unfolding of pitch over time." If you're not accustomed to listening for the six elements of music, melody is probably the one that grabs your attention. Melodies, or what we most often identify as songs, are tones of varying pitch arranged in reference to each other so that, when played together, they form a continuous musical idea.
Harmony results when pitches are stacked on top of each other and played simultaneously to make chords. Sequences of varying chords form progressions that fit together with the accompanying melody. When harmony and melody mesh well, the resulting music sounds pleasant or consonant, but when they clash the sound is dissonant or harsh. A balanced amount of harmonic dissonance is not always a bad thing, though; highly expressive musical styles like rock and blues make more emotional music out of occasional dissonance.
Like rhythm, form addresses the way music unfolds in time, but instead of focusing on the individual notes it describes how larger parts of a song fit together. In Western popular music, we use conventional names like "verse," "chorus" and "bridge" to describe song composition. Each part of the song is identifiable because it uses a consistent harmonic progression or melody. When the music switches to a different set of chords or alters its melody significantly, we know we are listening to a new part of the song. In classical music, form is notated with letters. A song with a melodic introduction, a variation and a return to the initial melody would be described as having an ABA form.
Texture describes how musical elements are distributed among instruments. To say a piece is thin in texture might mean it consists of a single melodic line unaccompanied by chords, which is called a monophonic arrangement. Homophonic arrangements pair the melody with chords. Polyphonic arrangements combine many simultaneously occurring melodies, creating a rich texture.
Timbre (pronounced TAM-ber) describes the tonal characteristics of instruments or combinations of instruments. A melody played on trombone will sound remarkably unlike the same melody played on oboe because the trombone's timbre is richer and rounder. Any grouping of instruments played together will create a unique timbre. Composers use variance in timbre to create contrast and melodic variation in their pieces. For an exercise in identifying timbre, listen to a recording of a symphony and notice the different tone qualities as new instruments play the main melody or theme.