Two distinct uses: abstract 'summon up' (鼓起勇气 'pluck up courage', 鼓起信心 'muster confidence') and literal 'bulge / swell' (鼓起肚子 'belly out'). Both come from 鼓 'drum' - picture skin pulled taut over a drum frame.
memory
鼓 originally pictured a drum being struck; the meaning extended to 'expand outward like a drumhead' → so 鼓起 = 'bulge up' physically or 'drum up' courage emotionally.
