Buddha-mind (Chinese foxing, Japanese busshin[1]) refers to bodhicitta, "[the] Buddha's compassionate and enlightened mind," and/or to Buddha-nature, "the originally clear and pure mind inherent in all beings to which they must awaken."[1]
Regarding awakening, Harold Stewart explains:
Busshin may also refer to Buddhakaya, the Buddha-body,[2] "an embodiment of awakened activity."[3]
Chan/Zen is also called foxin zong (Chinese) or busshin-shū (Japanese), the "Buddha-mind school."