What is the purpose or significance of devotion in Buddhism? Are there differences in acts of devotion in Mahayana and Theravada tradition?
In Theravada, there is faith and preferably verified confidence in the Buddha, the Dhamma and the Sangha. One who has faith is called a faith follower. There is faith, but there is no (Hindu style of) devotion in Theravada. There is however, reverence in Theravada Buddhism for example, through the act of prostration, as pointed out by ChrisW in the comments.
In Mahayana, some schools like Pure Land Buddhism, have devotion to Avalokiteshvara or Amitabha Buddha, with mantras to chant. There is a belief that one can be reborn in the Pure Land, the realm where the Amitabha Buddha resides, in order to continue the journey towards Buddhahood, with the guidance of Amitabha Buddha.
The Hindu style of devotion (bhakti) involve chanting the deity's names, remembering the deity's forms and glories, as well as having a close personal relationship with the deity. There are similar types of devotions in the Abrahamic religions. This is not found in Theravada Buddhism which does not have a Supreme God. Also in Theravada, the Buddha is no longer reborn after Nirvana. I am not sure if the Mahayana devotion in certains schools like Pure Land Buddhism is the same as the Hindu style of devotion.
Both Mahayana or Theravada emphasis on What to devote to, which has always been: The Buddha, the Dharma, and the Sangha.