The term buddhi yoga refers to action performed with a mental attitude of non-attachment to the fruits of one's action. Buddhi has the ability to discriminate between the real Self and the non-Self, and with such discrimination one can develop non-attachment to the non-Self.
A person with a dissipated mind is unable to comprehend the limitless joy that is experienced by the aspirant who is tranquil, performing his duties selflessly and skillfully. But when the mind is tranquil, pure reason (buddhi) is able to function. A tranquil mind alone has the capacity to maintain inner poise, which inspires and leads one to perform action skillfully and without attachment to the results. Such actions become a means for fulfilling the purpose of life. Whereas actions performed with selfish desire bind one to the objects of the world, actions done with non-attachment lead to complete freedom.
A disciplined mind and non-attachment are two important requisites for performing skillful action. If these qualities are absent, the mind is continually tossed by preoccupation with gain and loss, success and failure. Such a disturbed and distracted mind is not helpful at all; instead it is repeatedly a source of disappointment and can create misery, grief, and sorrow.
Skilled action is the gift of a disciplined mind, and non-attachment is the gift of buddhi yoga, the yoga of pure reason. Skilled and disciplined action and non-attachment are separated here only to enable one to understand the importance of both, but actually the two qualities go hand in hand.