The Jubilee legislation of Leviticus 25 generated two quite separate later religious institutions, one Christian and biblical, the other Christian and ecclesiastical, and neither is well known to be connected to the other or to the original Israelite law.
In Luke's Gospel, Jesus opens his public ministry in the synagogue at Nazareth by reading from Isaiah 61, "he has sent me to proclaim release to the captives... the acceptable year of the Lord" (Luke 4:18-19), and states that the scripture has been fulfilled in the hearing of those present. Isaiah 61 itself draws on Jubilee language, release, liberty, a proclaimed year, and many modern interpreters, especially in liberation theology, read the citation as a deliberate claim to be inaugurating something like a Jubilee, extended metaphorically to a comprehensive vision of restoration and social liberation, though the reading is contested by scholars who caution against assuming so specific an allusion in Isaiah's own poetic language.
Independently, the Catholic Church developed its own Holy Year, or ecclesiastical Jubilee, beginning with Pope Boniface VIII in 1300, who granted a plenary indulgence to pilgrims visiting Rome that year, an event that drew such crowds and income that the interval between Jubilees was progressively shortened, from a century to fifty years and eventually to twenty-five, still the schedule for the Church's ordinary Jubilees today, alongside occasional extraordinary ones. The ecclesiastical Jubilee borrows the biblical name, the theme of release reinterpreted as release from the debt of sin through indulgence, and a periodic cycle, but its actual content, pilgrimage and indulgence, has no counterpart in the Levitical institution beyond shared vocabulary.