by Danlee Mitchell and Jack Logan, Ph.D.

Meter is a result of the periodic effect of pulse (or beat) in music. Music does not require a pulse (or beat) to be music. Much music has no pulse. Music that does have pulse (or beat) always has beats that receive emphasis by being louder or longer than other surrounding beats.

To get a sense of how meter is created clap a steady beat with your hands. Begin clapping louder on one beat, and softer on the following beat. Repeat this pattern again and again. Try clapping two softer beats after the louder one. Try clapping groups of four, five and six.
The process of patterning beats with a stressed, accented beat (a louder and/or longer sound in comparison to other surrounding sounds) followed by a series of weaker beats is called meter. The stronger accented beat of a pattern (the louder or longer one) is called the downbeat. An accent of length is called an agogic accent. An accent of loudness is called a dynamic accent.
Meter is counted with Arabic numbers. Count one is known as the downbeat. Two patterns of two-beat meter (duple meter) are counted 1-2 | 1-2 (the "|" mark separates one group of two and the "_" mark represents an accent of loudness or length). Three patterns of three-beat meter (triple meter) are counted 1-2-3 | 1-2-3 | 1-2-3 | 1-2-3. Four patterns of four-beat meter (quadruple meter) are counted 1-2-3 4 | 1-2-3-4 | 1-2-3-4 | 1-2-3-4. Five patterns of five-beat meter (quintuple meter) are counted 1-2-3-4-5 | 1-2-3-4-5 | 1-2-3-4-5 | 1-2-3-4-5 | 1-2-3-4-5. Patterns may be created in this manner with any number of numbers limited only by practical considerations.
The most common meters in Western music are duple, triple and quadruple meters. Quintuple, sextuple and septuple meters (meters of five, six and seven) are also common in the West. Certain non-Western musics (for example, the music of India, Indonesia and Africa) use longer meters regularly.
One single pattern of any meter (for example, 1-2-3 4 of 1-2-3 4 | 1-2-3-4 | 1-2-3-4 | 1-2-3-4) is known as a measure. Music consists of a series of measures linked together to form a phrase much the same as a series of words are linked together to form a sentence. Most music is metered with periodic beats called regular meter. Some music features meter comprised of patterns of beats of different lengths called irregular meter. Dance music of eastern European Balkan states is comprised mostly of irregular meters and dance music of Greece features occasional irregular meters.
Meter is a very ancient musical element and extends back into human prehistory. Ancient poets may have borrowed the idea for metered poetry from musical meter. Say the words of your favorite pop song in rhythm and you will sense poetic meter as well as musical meter. Musical meter seems to have originated with the perception of the human heartbeat. Ancient songs were metered as well as the texts of ancient plays. Meter is a metaphor for all the periodic aspects of the human life experience.
Pre-Christian religions used meter in their music; however, with the advent of Christianity in the West, meter was disavowed for use during worship by the early Church fathers as pagan as was the use of musical instruments. Unmetered vocal chant replaced a variety of types of metered music and was viewed as the "voice of God" until the 12th century A. D.
Meter contains, as one of its various properties, pulse (or beat). The beat of a meter may be regular (patterns with the same lengths), or irregular (patterns with different lengths). Meters with a regular beat are called regular meters and meters with irregular beats are, not surprisingly, called irregular meters (also, "odd" meters).
Meter involves two other properties of music -- accent and periodicity. Musical "beat" is grouped into repeated patterns by accent involving the first beat of a particular unit of time (measure or bar). The first beat in a unit (louder and/or longer) is known as the downbeat. A downbeat delineates one unit of meter which is known as a measure or bar (interchangeable terms).
Measures of music have a periodic aspect to them in that they are repeated one after the other. Measures (units of time) are repeated while the material within measures (notes, rhythms, and others) change as the music develops.

Information provided by http://trumpet.sdsu.edu/M151/Elements_of_Music1.html