root is the starting point of a scale...

The mode is how the notes relates to the root and the other notes: for example major modes will have a third that will be 2 tones away from the root, while minor ones will be a tone and a half away... It goes on and on for every note.

most known modes Ionian (CDEFGAB in the key of C, or major scale) Aeolian (CDEbFGAB in C, it's the minor scale). If you raise the 4th in major, you get the lydian, etc. check out the tricks section, there's a lot about that.