Yoga exercise can be very effective when taught one to one, because each of our bodies are so different. One instruction could be perfectly understood by someone but not another just because we are all built in our own unique way. Private sessions are a great way to support your practice if you are feeling uncertain about any aspect of your practice. It can also support your practice through injury, learning to adapt the practice or try something completely new to enable you to continue practicing yoga.
For beginners is it a way to clarify your understanding about yoga pose alignment to enhance your group practice experience.
For experienced practitioners, it may be to learn a pose that you feel stuck in, to clarify something that you are unsure about or just to have a pair of eyes to check that you are not falling into any unhelpful practice patterns.
For teachers, private mentor sessions to discuss anything from practice to teaching.
It may also be helpful if you are suffering from some stress or anxiety and would like some private time to learn some tools to relax and manage the situation.