Best to give an example of the major modes:
Key of C-Major, scale is C-D-E-F-G-A-B-C.
1st mode: C-D-E-F-G-A-B-C (starting from 1st note of major scale) Ionian mode
2nd mode: D-E-F-G-A-B-C-D (starting from 2nd note of major scale) Dorian mode
3rd mode: E-F-G-A-B-C-D-E (starting from 3rd note of major scale) Phrygian mode
4th mode: F-G-A-B-C-D-E-F (starting from 4th note of major scale) Lydian mode
5th mode: G-A-B-C-D-E-F-G (starting from 5th note of major scale) Mixolydian mode
6th mode: A-B-C-D-E-F-G-A (starting from 6th note of major scale) Aeolian mode
7th mode: B-C-D-E-F-G-A-B (starting from 7th note of major scale) Locrian mode
All the modes have the same notes as the C-Major scale, they just start using a different note. Now, for each mode, using the 1st, 3rd, 5th (& 7th) notes, you'll form chords which are all related to the 1st mode chord. For example, using the 5th mode, the G major chord (G-B-D) is the V chord of the C major chord (C-E-G). If you were playing G/C/G chords, you can play a solo using notes from the 1st mode/5th mode/1st mode. In the end, they are all notes from the C-major scale.
There's lots more to discuss, but this is where to start.