The following introductory books' definitions don't distinguish meter from rhythm. Please see the titled question. I asked this on Music Fans, but I still don't understand. Please expound more plainly?
Many human activities, such as running, walking, or dancing, produce distinctive rhythms, which are often reproduced in music. Rhythm involves not only the positioning or spacing of notes in time, but also their duration, and both of these can be notated in Western music (see p.15).
The pulse (commonly known as the “beat”) is a regular unit of time around which the rhythm of a piece is organized. In a march, this would be the position in time of each footstep. The composer decides whether the pulse should be a half or a quarter, or any other note value. The speed of the pulse is the “tempo” of the work. Most composers have used Italian terms (see p.14) to indicate tempo.
The meter corresponds to the grouping of the pulse. Much Classical music is grouped in twos or threes. Each group is known as a “measure” or “bar” and in notation is separated by a “barline." The meter is indicated by a “time signature,” such as 3/4. The top number shows the number of beats in the measure, while the lower number shows the value assigned to each beat.
[p. 463] meter: the gathering of beats into regular groups
[p. 465] rhythm: the organization of time in music, dividing up long spans of time into smaller, more easily comprehended units
Rhythm is arguably the most fundamental element of music. Its primacy may result from our experience in utero; we heard the beat of our mother’s heart before we were aware of any sort of melody or tune. Similarly, our brain reacts powerfully and intuitively to a regularly recurring, strongly articulated “beat” and a catchy, repeating rhythmic pattern. Pop music derives its power primarily from the way it stimulates in the brain a direct, physical response to rhythm. We move, exercise, and dance to its pulse (Fig. 2.1).
The basic pulse of music is the beat, a regularly recurring sound that divides the passing of time into equal units. Tempo is the speed at which the beat sounds. Some tempos are fast (allegro) or very fast (presto) and some are slow (lento) or very slow (grave). A moderate tempo (moderato) falls somewhere in the range of 60 to 90 beats per minute. Sometimes the tempo speeds up, producing an accelerando, and sometimes it slows down, creating a ritard. But, oddly, we humans don’t like undifferentiated streams of anything, whether they proceed rapidly or slowly. We organize passing time into seconds, minutes, hours, days, years, and centuries. We subconsciously group the clicking of a seatbelt warning chime into units of two or three “dings.” So, too, with the undifferentiated stream of musical beats, our psyche demands that we organize them into groups, each containing two, three, four, or more pulses. The first beat in each unit is called the downbeat, and it gets the greatest accent, or stress. Organizing beats into groups produces meter in music, just as arranging words in a consistent pattern of emphasis produces meter in poetry. In music each group of beats is called a measure (or bar). Although music has several different kinds of meter, about 90 percent of the music we hear falls into either a duple or a triple pattern— duple meter or triple meter. We mentally count “ONE-two” or “ONE-two-three.” A quadruple pattern exists as well, but in most ways our ear perceives this as simply a double duple.
The time, or temporal (horizontal), aspects of music and the pitch (vertical) aspects of music are intimately intertwined and complement each other. This chapter concentrates on the essential concepts and terminology related to temporality. First, some basic terminology. Undifferentiated (e.g., same quality, loudness, and length) and equally spaced clicks or taps are called pulses. When you nod your head or tap your foot at a steady rate when listening to music, these pulses are called beats, because they now occur within a context that differentiates them; for example, some beats feel stronger than others. The tempo is the speed of the beat; that is, how fast or how slowly you nod or tap. Meter refers to the grouping of both strong and weak beats into recurring patterns. Rhythm refers to the ever-changing combinations of longer and shorter durations and silence that populate the surface of a piece of music. Rhythm is often patterned, and rhythmic groupings may divide the beat, align with the beat, or extend over several beats. The following discussion proceeds from temporal events that take place on the rhythmic surface of a piece to the metric grid that regulates the rhythmic surface.