Thanks for that important question:
The thumb provides the steady bass component that can really drive and support the song.
For instance, in the song Jambalya:
in playing in the key of D, the open strings - 4th string D and 5th string are your go to bass notes. With your thumb, ,pick the open D string (the root) initially and alternate with the lower A string. As the chord changes to the A chord, your bass notes become the open low A string with the open lower E.
The rhythm is constant on this 2 chord (D and A7) song with a "1 and 2 "count beat. (hit those bass notes on the 1 and 2 ) Let your picking hit immediately in between these driving bass notes.
Lastly ,listen to the song to hear and feel that driving bass.
"pick guitar-fill fruit jar!"
Have fun with it and i hope this helps.