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Bodhicitta means awakening-mind, from 'bodhi' meaning awakening and 'citta' meaning mind or consciousness. In Mahayana Buddhism, three aspects liberate one from cyclic existence: the attitude of renunciation (which turns away from worldly attachments), the wisdom of emptiness (which sees object without grasping at intrinsic existence), and finally bodhicitta, which is the intention to help all sentient beings.
Bodhicitta is of two types: first, the very intention and aspiration to free all sentient beings from suffering; second, the process and implementation of doing so. Bodhicitta is also categorized as relative and absolute, where relative bodhicitta implies a compassionate wish and striving to help others, and ultimate bodhicitta is seeing the empty nature of things. I believe this is linked with either training compassion or gaining compassion through wisdom.
There are various ways of training bodhicitta. Among these, one may train the four immeasurables: loving-kindness (wishing for others' well being), compassion (wishing to alleviate others' suffering), sympathetic joy (partaking in others' well-being), and equanimity (considering others equally). Other means exist in Buddhism to develop bodhicitta, as equalizing oneself and others, which involves going past the distinctions between persons via an understanding in emptiness. Also, seeing all beings as one's mother relies on an understanding of karma to conceive others as having helped us in past lives.
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Relative to your question, bodhicitta is not nirvana as it relies on worldy attachment (i.e. compassion) to occur. I understand, though I'm unsure, that you're asking if it is felt or cognitive. Interestingly, the Dalai Lama has said its best to focus on feeling when generating compassion, after having produced reasons. And, I have read a scientific papers 1 2 claiming the value of both motivational/affective aspects and cognitive aspects of compassion meditation. So, both components are clearly experienced in compassion.
More so, given that the union of compassion and emptiness is the aim of the Mahayana, and that emptiness entails initially an analytical training, one might consider how compassion merges with cognitive processes to see the world differently. So, it is indeed felt and realized.
Finally, given emptiness is related to non-duality, I feel the separation between cognition and feeling is illusory, as everything is highly related via cause and effect.
Hope this helps!