[office of their ministry]: The “ministry” is the thing that the angels do on earth. The “office of their ministry” refers to their divine assignment. The angels appear because they are sent to us, and the “office of the ministry” simply indicates the job that they are to do.
[to call men unto repentance]: This is the work of the angels. They are to call men to repentance. Of course they typically do not call individuals to repentance, leaving that task to the prophets and other men (and women) called of God for that purpose. However, they do at times directly intervene, as with Paul and Alma the Younger.
[to fulfil and to do the work of the covenants of the Father]: Angels come to earth on assignment from the Father, to do that work which is part of the goals of the Father. They assist in fulfilling the covenants because God has promised that he will pay attention to us, and provide us the opportunities to lay hold of the blessings of the gospel.
[to prepare the way among the children of men, by declaring the word of Christ unto the chosen vessels of the Lord, that they may bear testimony of him]: The most typical way in which the angels fulfill their function on earth is to communicate with the “chosen vessels fo the Lord” who are the prophets and others who can then bear firm testimony to the rest of us.