the word "rainbow" is used too much in MLP especially considering it's already a name of one of the MCs, so it's now called Harmony Power! Each time the mane 6 use the elements of harmony or their magic friendship blast, these harmony forms are unlocked. Most of it isn't permanent, but after defeating Tirek, the harmony power permanently stained their manes with one streak of color. (Yes, even Rainbow Dash, you just can't see it because her mane is already rainbow.)

Twilight Sparkle's white glowing eyes make many appearances in the show when she powers up or uses strong magic - this is actually Twilight being temporarily possessed by the spirit of Harmony, who normally resides in the tree. (you know, that freaky glowing astral twilight that appeared to the young six under the school of friendship?)

See everyone separately here: https://www.deviantart.com/itsvoids/journal/Harmony-Power-Each-Vector-Separate-912398345