There is no definition of yoga more famous (or arguably more efficient and useful) than the first one offered in the Yoga Sutra of Patanjali: yogaś-citta-vṛtti-nirodhaḥ. A rough translation: yoga is the restraint of the turnings of the mind. To put it still more simply: yoga is the cessation of thought. This is a definition that functions like an ideal: according to it, most of us are not practicing yoga, we aspire to yoga. We learn and practice various techniques out of a desire to experience this stilling of the mind. There isn't much to be said about what happens when yoga is achieved: it is a state beyond the rational mind, thus rendering language pretty useless in describing it.
Frankly, this definition of yoga doesn't really come alive for me without yoga's corresponding definition of the mind. It is a fundamentally different definition than the one we're used to in the world of Western philosophy, which by and large positions mental cognition as a component of the essence of identity and soul. In yoga philosophy (or to speak more accurately, Sankhya philosophy, which is the philosophical system upon which yoga practice is built), the mind is something totally separate from the soul, or the pure consciousness, at the core of every being. The mind is like a subtle organ: invisible but nonetheless an anatomical structure that is intrinsically functional, not unlike the bladder, the nose, or the heart.
From this perspective, thoughts are vrittis, or "fluctuations." As the beating of the heart is the movement of the heart, the generating of thought is the movement of the mind. So, although thoughts may at times be brilliant, powerful, even enlightened -- they are always superficial to this mystical state that yoga postulates is beyond them. Whatever the highest states of samadhi or deep meditation are like, it is clear, according to Patanjali, that they do not involve thinking as we normally understand it.
As such, yogis tend to give thoughts -- vrittis -- a really bad rep. So many of us (myself certainly included) are at very early stages of practice, and yet we're inspired by the mystery of the awareness beyond the mind, and in our rush to get there we essentially dismiss the value of thinking. Most damagingly, we may marginalize any and all of our thoughts as elements to be discarded on the path toward illumination. But this unwillingness to walk the path from point A to point B has dire consequences for each of us individually, teaching us not to use the power of our intellects, and catastrophic consequences for us as a community. A few years ago, when I was starting develop my yoga practice, I was certainly unnerved by this tendency in the yoga community to dismiss intellect (and I still am). Coming from an academic and artistic background, I was taught at an early age to love thinking deeply. Many of my most valued experiences in this world involve the encountering of wild, transformative thoughts and thinkers.
Even though the deeper states of yoga imply states of mind where thought has come to a point of cessation, it is not an anti-thought practice. And so, the discipline of yoga is not an anti-intellectual discipline; it is, in a sense, the perfection of the art of thinking, of inquiry... rather than just giving up [and thinking], 'well, thought has gotten us into all of this trouble, so now we're not going to think well at all.' What is astonishing is how easily this is misinterpreted by people who find deep thought to be too much of a strain, and so they're unwilling to wrestle with its paradoxes.