Yoga means union of the outer self with the inner self. It can be attained through many paths such as Karma (action), Bhakti, Sankhya (awareness), Buddhi (intellect) and so on. Depending on one’s nature, one attains yoga through means suited to them.
Krishna tells Arjun (2.49) to seek refuge in buddhi as motivated karma is far inferior to buddhi yoga and miserable are they whose motive is to obtain the fruits of action. Earlier, Krishna said (2.41) that in karma yoga, the buddhi is coherent and the intellect of those who are irresolute is bahu-shakha (many-branched).
Once Buddhi attains coherence (like a magnifying glass focuses light) it's capable of any intellectual journey. Any journey, including the journey towards self, involves direction and movement. Krishna’s reference to buddhi yoga here is about the direction of the journey towards the inner self. Usually, we use coherent intellect to fulfil desires in the outer (physical) world, but we should use it to pursue our journey towards the self.
The first signs of using coherent intellect for internal journey are when we start questioning everything like our deep rooted beliefs, emotions, assumptions, thoughts, actions and even the words we speak. Just as science uses questioning to push the frontiers of knowledge, the same questioning leads us to uncover the supreme truth.
Krishna further says that miserable are they whose motive is to obtain the fruits of action. We develop this tendency as the fruits of action give us pleasure. But in a polar world, every pleasure soon turns into pain in the due course of time, which increases our misery.
Krishna nowhere promises to shield us from polarities but tells us to use buddhi to transcend them to be atmavaan (established in self). It's neither knowing nor doing, just 'being'.
Source - Daily World