Meter is indicated in music notation with time signatures, which consist of two numbers: a top number, and a bottom number. These numbers establish the relationship between the beat and the written rhythms.
The bottom number of a time signature stands for a rhythmic value - means half note, means quarter note, means eighth note, and so on (see Rhythm for more details). The top number indicates how many of this designated note will constitute a measure. That is, a measure contains two quarter notes, a measure contains two half notes, and so on.
So, what is the relationship between these groupings and the beat? To answer this, first we must discuss simple meter and compound meter.
In simple meter, the duration of note indicated by the lower number will almost always corresponds with the beat. For example, in time there are three quarter notes in a measure, and the conductor (or metronome) will beat each of those three quarters. To put it another way, if the orchestra were to play only quarter notes, they would play one quarter note for each click on the metronome or beat of the conductor's baton.
As a second example, in time, the conductor's beat would correspond with the half note instead, and there would be only two clicks per measure. In this case, if the orchestra were to play only quarter notes, they would play two for each beat. Thus, if the conductor were to beat exactly the same tempo (beats per minute) as he had for time, the piece would essentially go twice as fast.
In compound meter, things get a bit more complicated. In a measure of (a common compound meter), there are six eighth notes. However, a conductor will almost always beat only two beats per measure instead of six. Thus, time is analogous to time. Perhaps became the standard instead of because there is no convenient numerical representation for a dotted quarter note. Whatever the case may be, this same convention applies to all compound meters. is the same as , is the same as , and so on.
You may have noticed that if (dotted quarter) is the unit of the beat, then each beat will contain three (eighth notes), making them feel like triplets. This is the fundamental difference between simple and compound meter: in simple meter the division of the beat is duple (two equal parts), whereas in compound meter the division of the beat is triple (three equal parts).