Music based on major and minor scales came into common usage in the early 1600s, and of course we have been using them ever since. In the Western world, babies start hearing them in the womb and get thoroughly acclimatised to scale-based in infancy.  Folk tunes and nursery rhymes see to that!

But before the 1600s, composers wrote in modes. Modes went underground for a while but re-emerged in jazz and the music of  Debussy and Vaughan Williams.

If you listen to Indian raga, Gregorian chant, some early French or Spanish carols, you are often listening to modal music

Alleluia Angelus Domini, recorded by Dominique Vellard on harmonia mundi HMC905261, in the Dorian mode

Scarborough fair, recorded by Celtic Woman, in the Dorian mode

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If you sit down at a piano keyboard and play a scale using only the white notes, and starting on middle C, what you get is the familiar C Major scale, right?  Well yes, but this is actually a mode - the Ionian mode. 

Starting on one of the other white notes will produce a different mode, and each has its own distinctive sound. These are their names, along with the starting note:
  

Mode Name	Starting Note	Notes Used
Ionian (Major)	C	c d e f g a b
Dorian	D	d e f g a b c
Phrygian	E	e f g a b c d
Lydian	F	f g a b c d e
Mixolydian	G	g a b c d e f
Aeolian (Minor)	A	a b c d e f g
Locrian	B	b c d e f g a

A tune could be written in each of these modes in turn and in each case, it would appear as if the tune were in C (no sharps or flats). Just looking at the key signature (number of sharps/flats) of a modal tune will not tell you much about its mode.

Try  improvising in different modes.  Start with short sections of the mode played as a run, and keep circling back to the 'home' note, playing only whole notes at this stage.  As you gain confidence try to add harmonising notes or chords in the left hand.

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Each mode can be played starting on any note, but then some black notes are needed to get the combination of tones and semitones which gives the mode its distinctive sound.  For example if we put the seven modes in each case starting with C we get a variety of keys: 

Mode Name	Notes	Pattern	Key signatures
Ionian	C D E F G A B	1 2 3 4 5 6 7	No flats or sharps
Dorian	C D Eb F G A Bb	1 2-3 4 5 6-7	Bb Eb
Phrygian	C Db Eb F G Ab Bb	1-2 3 4 5-6 7	Bb Eb Ab Db
Lydian	C D E F# G A B	1 2 3 4-5 6 7	F#
Mixolydian	C D E F G A Bb	1 2 3-4 5 6-7	Bb
Aeolian	C D Eb F G Ab Bb	1 2-3 4 5-6 7	Bb Eb Ab
Locrian	C Db Eb F Gb Ab Bb	1-2 3 4-5 6 7	Bb Eb Ab Db Gb

Today only two modes (major and minor) are in common use in mainstream music. The most common modes, in folk and traditional music are: Ionian, Dorian, Mixolydian and Aeolian.

Scarborough fair, recorded by Celtic Woman, in Dorian mode

The remaining three are known as the rare modes, and are almost never used.

The Phrygian mode survives in Andalucian music from Spain, its flattened second conjuring great longing and melancholy, with  echoes of the call to prayer from Moorish minarets:

Ven Querida, recorded by Dominique Vellard, in Phrygian mode

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