What determines the key is the key centre. The key centre is the note (and the chord built upon it) in a song. that, when we hear it, sounds like the HOME note and chord that we always want to return to.
When we hear that note and chord, especially at the end of verses and choruses, it sounds strong, stable and often final. That's why almost all songs finish on that note. Only the key note and chord can give that feeling of finality.
For example, take the song Happy Birthday. Listen to how final it sounds when the last note is sung "YOU". It sounds like that, not because it's the last note but because it's the key note. (Try ending on any other note.)
What makes the keynote sound special is the way that all the other notes relate to it.
If I wanted to write a song with the note C as the key note, then my first choice of notes and chords would be from either the C major scale or the C minor scale.
Both of those scales have sets of notes that will make C sound like the keynote - but they will have a very different feel. If I use the notes of the C major scale my song will sound brighter than if I used notes of the C minor scale.
To indicate which set of notes is used, the song is said to be in the key of C major or C minor depending on which scale was used to provide the notes and chords.
Other sets of notes apart from those scales can be used too - and those are the modes (They're not so good at it as the major and minor scales, though).
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