JOEL - Jesus set the example about being about the business of God:

"And he said unto them, How is it that ye sought me? wist ye not that I must be about my Father’s business?" (Luke 2: 49)

Anything Jesus did was His Father's business.
We do the business of God by representing Him among all people, preaching the gospel, and administering the ordinances. Chosen servants and appointed officers in the Church are put on earth by him to conduct the work necessary for the salvation of mankind. The Lord said, "This is my work and my glory, to bring to pass the immortality and eternal life of man." (Moses 1:39.)
A minister called of God, as was Aaron (Heb. 5: 4), and endowed with the holy priesthood, represents the Lord when he is performing his official duties, and is the Lord’s agent.

"Wherefore, as ye are agents, ye are on the Lord’s errand; and whatever ye do according to the will of the Lord is the Lord’s business." (D&C 64: 29)

President Harold B. Lee said:
"When one becomes a holder of the priesthood, he becomes an agent of the Lord. He should think of his calling as though he were on the Lord’s errand. That is what it means to magnify the priesthood. Think of the Master asking each of you, as this young boy did of Joseph and Mary, Wist ye not that I must be about my Father’s business? Whatever you do according to the will of the Lord is the Lord’s business." (Harold B. Lee, Stand Ye in Holy Places (1974), 255)

Of course being on the Lord's business is not restricted to those holding the priesthood. Anything that any member does to bring to pass the three-fold mission of the church(preach gospel, perfect saints, redeem dead) is on the Lord's business.