You mostly use your triceps when you try to extend tour arm, or push something away. So in everyday life, you use it less than its counterpart (the biceps) that you use to carry or lift something. It can lead to unbalance in your elbow and pain.
Plus I often hear ladies complaining about the "flappy" part of their arms...
So here it is: how to work on your triceps without equipment.
The first thing is to be able to do a knee plank, holding position with your abs engaged.Then put your hands straight under your shoulders, fingers pointing foirward. And finally, make sure that your elbows are bending backwards (not out). Even with a small bend (as shown in step 1), you will feel it if you put enough of your body weight forward. Don't slide your butt backward to put your body weight on your knees. This is cheating! lol.
Instead, focus on the pressure going through your arms.
Don't hesitate to contact me for any questions.