Blue eyes is the Normal Real Alice as Master Puppeteer. Golden Eyes is Awakened Alice as the Mistress of the Grimoire. Red Eyes is a sealed persona of Alice as the Princess of Makai.
Although, I personally don't understand them, mainly because of the japanese song. The one thing I hate about songs with japanese lyrics is that there are wayyyyy too much syllables.
I liked that video where Alice was doing a love scene with a life size Marisa doll and was caught by Reimu, Marisa and Yuyuko. Reimu did tell Marisa that Alice might kill you one day.