Basically, modes come from a major scale, also known as the Ionian mode. This is your TTSTTTS spacing, note by note, as in Cmaj: CDEFGABC.Starting on the 2nd note, and rising to an octave above it, you get the Dorian mode.The next starts on the 3rd note, E in this scenario.It's the Phrygian mode. The 4th degree start gives the Lydian, the 5th Mixolydian.Start from the 6th (A) and it's the Aeolian, leaving an odd sounding set of notes, not used too often, called the Locrian mode.
Each of these modes contain the same notes, as seen above, but they work because each 'centres' around its start note e.g. G mixolydian has G as its root.That's why it sounds dominant - it has a flattened 7th compared with the major scale, which is used as our datum point.
Going back to that major scale - if we flatten just the 3rd note, we get an ascending melodic minor.This can then be used to make a new set of modes, each one starting on a different scale note.
Start on the 5th degree of this melodic minor scale, and you've found your Aeolian Dominant.A.K.A. Mixolydian b6, Hindu and Aeolian #3, amongst others.
More importantly, and more advanced, are the chords that each degree of any scale will provide.As triads, the major scale will give, in turn, maj, min,min, maj, maj,min,dim.
Take this on to the Aeolian Dominant, and it gives: maj,dim,dim,min,min,aug,maj.Obviously these chords will give a very different flavour to a song containing them compared with the set used for major/Ionian.
The Phrygian Dominant you mention is similar in that it takes its notes from the Harmonic minor, starting at the 5th degree, but the mixes of notes to give the chords are different.
All this is really not starter theory, but I hope it answers your question.As to why it's called Aeolian, which is the 6th degree of the major, don't know yet.