Jude starts his reason for writing by addressing the "Beloved". This shows he had a close relationship with his readers, and cared for them greatly. When Moses is blessing the tribes before his death, he calls Benjamin the beloved of the LORD [Benjamin was closest to his father], and says that they will "dwell in safety" because they are in His presence. Daniel was also beloved of God, and God sent him visions and interpretations as a result (Dan. 9:23, 10:11, 19). In Nehemiah 13:26 it states that Solomon was beloved of God: this is why he became king, rather than David's first son. Above these, Christ was beloved of God; this was spoken after the Lord's baptism (Matt. 3:17; II Pet. 1:17). Paul also mentions a couple men as beloved (Col. 4:16, Philem 16).
The application: God's beloved people over all of time had been, and still are, the Hebrew people. But with Christ's finished work, we are now "accepted in the beloved" (Eph. 1:6). Christ has made us all one in Him. As part of this, the Bible tells us to not lose any "beloved sleep", or to waste any part of our lives, but to spend it in pursuit of God (Ps. 127:4). Through the application of Song of Solomon, the Word of God also tells us that Jesus is our beloved.