Bar or measure

Music is normally divided into equal time-lengths called bars (or, in some countries, measures - see alternative names), each consisting of the same number of beats.
The time signature gives the number of beats in a bar and the type of beats, so it tells you how long each bar is (in terms of the number and type of notes and/or rests in a single part in that bar).
Bars dividers, called bar-lines, are indicated in a score by a vertical line from the top to the bottom of the stave. A double bar-line is written at the end of a piece: . The double bar-line is sometimes written with the second line thicker than the first; this is normally used at the very end of a piece, and two equal lines are used at the end of sections.
Bars give an intuitive division of a piece of music into manageable chunks; the strongest accents come on the beat immediately following a bar line, so it is relatively easy to count bars, and it should be easy to count the beats within each bar.
The number of bars in a section of music is often regular; four bars often make a short phrase, eight bars and sixteen bars are often the section sizes next largest. These numbers feel "natural"; a section of 17 or 19 bars often feels "wrong". This is because of a hierarchical structure of beats strengths that we naturally feel; there is a strong accent on the beat at the beginning of every fourth bar, an even stronger one at the beginning of every eighth bar, and so on.