The modes are sectors or excerpts (with the span of an octave) from a diatonic 2-octave scale starting with A (a). There are always two modes that fit together. they are related via the "Finalis"(finishing note). The halftones are always between e and f and between b and c. the modes are not scales in the strict sense of the word. they are just fragments of scales that encapsualte the note-material of melodies used as model.
There are Authentic (original) and Plagal (derrived) modes. The authentic modes are formed over the finalis. the plagal modes do have the finalis in the middle of the "scale". as I mentioned above, there is for every authentic mode an according plagal mode. You can easily find it by taking the finalis of an authentic mode and go 4 notes down - thats the first tone of the relative plagal mode. The authentic modes are called Dorian, Phrygian, Lydian and Mixolydian. The plagal modes have an added sylable "Hypo" infront (eg: hypodorian). Furthermore there are the modes Aeolean and Ionian. these two modes correspond to todays A-minor and C-major. When you build a mode on B it is called lokrian.
The modes have already been used (without him knowing it) in the 4th century by Ambrosius of Milano. Pope Gregor the great was the first to sysematically sort the different forms of choral music which made it more easy and standardized. this was in the 6th century and thats when famous choral-schools developed like Paris, Metz, Aachen and Mainz. Aurelianius Reomensis was the first to give he modes their old names (9th century) - Protus authentus and Protus plagalis. In the 10th century the names of the single modes where added and in 1547 H. Glarean added the above mentioned aeolean and ionian modes.
The modes where the musical and theoretical basis fr medieval music. they lost their importance at the end of the 16th century because major and minor got more and more dominating. in the 19th and 20th century the modes have made a revival in art-music and especially in jazz.
The modes have been developed in the gregorian chant. It is not the half-steps that characterise the modes but melodical phrases. The modes are (as a novelity) linked to the finalis. Modes are - because of their simplicity - very good to accompany vocal music melodically. The melody was not the imortant part - the important part was the lyrics. The melody was only making the text easier to learn and it was easier to transport the meaning and feeling when it was sung. A good example where the minnesingers. It was basically vocals that where used to attract women - and that was easier when accompanied by music (mostly only a simple melody with one instrument). And thats where the modes where used too. And a short list:
Dorian (d' - d'') Hypodorian (a - a')
Phrygian (e' - e'') Hypophrygian (h - h')
Lydian (f' - f'') Hypolydian (c' - c'')
Mixolydian (g' - g'') Hypomixolydian (d' - d'')
Ionian (c' - c'') Hypoionian ( g - g')
Aeolian (a' - a'') Hypoaeolian (e' - e'')
Lokrian (h - h`)