For reasons that are sometimes all too obvious, armpits are an often maligned part of the anatomy.  Perhaps if we referred to armpits by their anatomical name, axillae, we would be more cheerfully disposed toward them. I find I feel more friendly about my axillae since I discovered the word is diminuative of “ala”, wing.
Axillae are absolutely crucial to many yoga poses. Take adho mukha svanasana, as an example.

Down Dog

This photo of me was taken in my pre-armpit-activating period. It’s a reasonably good pose but could have been hugely improved if I’d switched on the muscles at the front and back of my armpits. At the front, pectoralis major aids with the chest opening and stabilizes the shoulder joint. At the back, latissimus dorsi activation will help you connect with your abdominal muscles, so it is also useful in a posture like Navasana.

Paripurna navasana

If you can’t figure out how to get these areas working, think of squeezing lightly and equally at the front and back of your armpits when doing these two poses. Avoid tightening too much or you’ll narrow the front and back chest, creating tension in your neck.
American yoga teacher, Donald Moyer suggests bringing the outer edges of your shoulder blades more firmly onto the side ribs. This is a great adjustment for your pranayama practice too.
If you are a teacher with a middle age population attending your classes, you need to encourage the students to stabilise the shoulder girdle. Otherwise, you may see students turning up with shoulder problems, i.e., rotator cuff tears or impingement of the shoulder joint.

On another topic, a friend sent a particularly lovely youtube link. Well worth the twenty minute investment of your time.