taru-adjective, adverb taking the 'to' particle
continuous; unbroken; ceaseless
Describes something that continues steadily and strongly, often with a sense of underlying vitality or flow, like a pulse. Commonly used with と as an adverb.
彼の情熱は脈々と受け継がれている。
His passion has been passed down continuously.
この川は山から海まで脈々と流れている。
This river flows ceaselessly from the mountains to the sea.
絶え間ない is a more common, everyday adjective meaning 'incessant' or 'uninterrupted', while 脈々 is more literary and emphasizes a steady, vital continuation.
Reduplication of 脈 (みゃく, 'pulse' or 'vein'), suggesting a continuous, pulsing flow. The exact historical derivation is uncertain, but the form is a standard literary adverb.