It's semi-arbitrary. In a song where the chords change regularly and evenly, they often correspond with a bar, a bit less often two bars or half a bar. Is usually makes up 4 notes of the "normal" length for that piece, but this is not adhered to as time signatures can be any size. But 4 is typical. A march is 4/4 (literally, four quarter notes per bar). A waltz is 3/4 (three quarter notes).
The "normal" note length depends on how the melody is written. Something like Beethoven's fifth has an overwhelmingly majority of notes all the same length (a quarter note). Something from Madonna will have a much wider variation of note lengths.
Bars are often grouped, though there's no notation for that. A song phrase (e.g. a single 'line') will often be 4 or 8 bars. A song section, say, a verse or a chorus, will often have a multiple of four bars - e.g. 12, 16, 20, etc. A 'long' note or a pause at the end of a chorus, for example, is likely to be an extra bar. You can sometimes feel the rhythm of the song take a double-step when that happens.
It's quite tricky to explain if you don't read music. :-)
Wade, who is a muso, if you hadn't realized.