Albert Barnes on Luke 4:19

To preach the acceptable (q) year of the Lord. The time when God is willing to accept of men, or to receive sinners coming to him. The gospel assures us that the guilty may return, and that God will graciously receive them. There is, perhaps, here, an allusion to the year of jubilee--the fiftieth year, when the trumpet was blown, and through the whole land proclamation was made of the liberty of Hebrew slaves, of the remission of debts, and of the restoration of possessions to their original families, Lev 25:8-13. The phrase "the acceptable year" means the time when it would be acceptable to God to proclaim such a message, or agreeable to him---to wit, under the gospel.

(q) Isa 61:2, 63:4