Travis picking is a fingerstyle where the thumb never stops: it plays a steady quarter-note bass, alternating between two strings, while the fingers add notes between the beats. Think of the thumb as a drummer.
This lesson is in C major with C and G in open position. On C, the thumb plays the 3rd fret of the A string, the 2nd fret of the D string, then the 3rd fret of the low E (move your ring finger from the A string to the low E and back), then the D string again. On G it rocks between the 3rd fret of the low E and the open D. Palm-mute the bass strings lightly with the edge of your hand so the bass thumps instead of booming.
Then add the fingers: a pinch on beat 1 that rings through its "and", then i and m on the "and" of beats 2, 3 and 4.
Common mistake
Letting the thumb follow the fingers. When a finger plays, the thumb tends to stall or double up. Keep the thumb part identical to exercise 1, whatever the fingers do.
Practice the thumb alone while watching TV. When it runs without thought, the fingers become easy.