It's not easy to distill the essence of yoga down to a couple of sentences. Ancient scriptures like the Bhagavad Gita speak about yoga being the study of the Self; yoga as evenness of mind; yoga as skill in action.
Patanjali in his Yoga Sutra says: "Yoga is the cessation of the fluctuations of the mind."
In the words of BKS Iyengar:
"Yoga allows you to achieve a sense of wholeness in your life where you do not feel like you are constantly trying to fit the broken pieces together. Yoga allows you to find an inner peace that is not ruffled and riled by the endless stresses and struggles of life. Yoga allows you to find a new kind of freedom that you may not have known existed."