This mode is a major scale that starts on a note that isn’t its root. Yes, the Mixolydian mode is exactly the same as the major scale - it just begins on the fifth note.
For example, C major (C D E F G A B) gives you G Mixolydian (G A B C D E F). And, though the notes are identical, reordering them means the gap (aka interval) between the root and the seventh note is different. The details are explained below. Check out Lynyrd Skynyrd’s Sweet Home Alabama as a great example of a chord progression and riff in D Mixolydian.
1. C Major and G Mixolydian scales
You can see here how C major and G Mixolydian have the same notes but differ on one vital interval - their 7ths: C and B are 11 semitones apart (known as a major 7th); G and F are 10 semitones apart (a minor 7th, aka b7th). That’s enough to give the Mixolydian mode a more laid-back vibe than the bright, happy-sounding major scale.
Here we're playing C major and G Mixolydian. Play through the scales and see how they use the same notes. All that changes is that G is the root note in G Mixolydian.
2. Chords in the Mixolydian mode
The root chord in the Mixolydian mode is the dominant 7th (G7 if in G Mixolydian). Why? The notes that make up the chord come from the mode: G7 (G B D F) takes its notes from G Mixolydian (G A B C D E F). If in C major (C D E F G A B) your root chord would be Cmaj7 (C E G B). The different 7th intervals make it happen.
This punky riff uses G, C and F chords. It doesn’t matter that we’re playing G and not G7. All the notes of G Mixolydian are used and you can hear that G is the root chord.
3. Mixolydian lead lick
Just like our rhythm part, all the notes of G Mixolydian are used here. What makes this a Mixolydian line and not one of the other modes of C major is simply that we’re treating G as our root. The music feels somehow complete (aka ‘resolved’) when you reach the final G note of our lick and the backing music lands on the G chord shortly afterwards.