Memor erit in sæculum testaménti sui: virtútem óperum suórum annuntiábit pópulo suo:
He will be mindful for ever of his covenant: He will show forth to his people the power of his works.
Memor erit in sæculum testaménti sui = he will be mindful/remember forever of his covenant
virtútem óperum suórum =the power of his works = his mighty works
annuntiábit pópulo suo = he will make known/announce/show forth/will declare to his people
We can see this verse as summarizing both the Old and New Testaments.
First let us consider the Old. St Robert Bellarmine points to the carrying through of God’s Covenant with Abraham chronicled there:
“…that is, by his constant providence and protection, he will show that he is mindful of his covenant and his promises. The principal point in the treaty that God made with Abraham was, that he should give his posterity the land of the Chanaaneans, which was, consequently, afterwards called the land of promise. He, therefore, shows how "he is mindful of his covenant," when he says, "he will show forth to his people the power of his works;" that is to say, bearing his promise in mind, he will display his power to his people, by turning back the waters of the Jordan, by levelling the walls of Jericho with the sound of the trumpet, by stopping the sun and moon at the command of Joshua, by raining down stones from heaven on the enemies of the Jews, and by many other similar miracles.
But of course, the New Testament is the more complete fulfillment of the Old, and one can pray this daily as we say the Benedictus (Luke 1:72) at Lauds: “to perform the mercy promised to our fathers, and to remember his holy covenant”.
Cassiodorus takes up this theme, and argues that the verse is fulfilled in the Gospel with the miracles Christ performed, and communicated to St John the Baptist:
“The thought contained in the three verses is here filled out. The power of his works is that which he states in the gospel: The blind see, the deaf hear, the lepers are cleansed, the dead rise again, and blessed is he that shall not be scandalised in me. He has announced, in other words, made plain, that is to the Christian people whom He redeemed with His precious blood. They express this with the spirit of prophecy, for with holy faith they believed in the Lord before His coming. He gave them the inheritance of the Gentiles when He fashioned the Catholic Church from living stones from all nations. This is the inheritance promised to Abraham: I will multiply thy seed as the stars of heaven, and as the sand that is by the sea-shored They revealed the reason why he announced to his people the power of his works; it was to give them the inheritance of the Gentiles. It was the purpose of the miracles that they should believe, and by believing obtain the promised rewards.”
memor, oris mindful of, thoughtful of; to remember, call to mind, think of, take thought for, recall, recount, etc.
testamentum, i, n. a covenant, testament
virtus, utis, f strength, power, might; an army, host; annuntio, avi, atum, are to announce, proclaim, publish, make known.
populus, i, people; the chosen people; a heathen nation
Notes on the next verse can be found here.