Wikipedia
Monoenergism is a Christian heresy related to and often paired with monophysitism.
In the 7th century, after the failure of Justinian I and the Second Council of Constantinople to mend the Chalcedonian schism and unify the empire by a single Christology, the emperor Heraclius attempted to solve the schism between the orthodox Chalcedonian party and the monophysite non-Chalcedonian party, suggesting the compromise of monoenergism. This compromise adopted the Chalcedonian dyophysite belief that Christ the Incarnate Logos of God is of and in two natures, but tried to address monophysite misgivings by the view that Christ had one "energy" ( energeia), a term whose definition was left deliberately vague. Monoenergism was accepted by the Patriarchs of Constantinople, Antioch and Alexandria, as well as by the Armenians and was not criticized by Pope Honorius I of Rome. However, the strong opposition of Patriarch Sophronius of Jerusalem won wide support. This led Heraclius to abandon the teaching in 638 and to attempt to enforce instead the doctrine of monothelitism, opposed most notably by Maximus the Confessor. This too failed to heal the schism and theologically unite the Empire.
Both monoenergism as well as monotheletism were condemned as heresies by the Sixth Ecumenical Council, held in Constantinople in 680.