1) to publicly admit one's guilt;
2) to publicly declare one's faith;
3) to privately admit one's sins to a priest or to God.
The Bible has three words which are translated "confess":
1) the Greek ἐξομολογέω (exomologeō), which means "to acknowledge openly" (Rom. 14:11; 15:9; Phil. 2:11; Jam. 5:16);
2) the Greek ὁμολογέω (homologeō), which means "to agree with" (Mt. 10:32; Lk. 12:8; Jn. 9:22; 12:42; Acts 23:8; 24:14; Rom. 10:9; 1 Jn. 1:9; 4:15; 2 Jn. 1:7); and
3) the Hebrew word יָדָה (yadah), which means "to verbally declare one's guilt, or to praise, etc. (Lev. 5:5; 16:21; 26:40; Num. 5:7; 1 Kg. 8:33, 35; 2 Chron. 6:26; Neh. 1:6; Job. 23:8; Ps. 32:5).
Confess publicly that Jesus is the Son of God
"Whosoever therefore shall confess Me before men, him will I confess also before My Father which is in heaven. But whosoever shall deny Me before men, him will I also deny before My Father which is in heaven" (Mt. 10:32-33).
Confess publicly that Jesus died for your sin, and rose to be your Lord
"For I delivered unto you first of all that which I also received, how that Christ died for our sins according to the Scriptures; and that He was buried, and that He rose again the third day according to the Scriptures" (1 Cor. 15:3-4).
"That if thou shalt confess with thy mouth the Lord Jesus, and shalt believe in thine heart that God hath raised Him from the dead, thou shalt be saved. For with the heart man believeth unto righteousness; and with the mouth confession is made unto salvation" (Rom. 10:9-10).
Confessing Him as Lord means repenting from sin
"When Thy people Israel be smitten down before the enemy, because they have sinned against Thee, and shall turn again to Thee, and confess Thy name, and pray, and make supplication unto Thee in this house: Then hear Thou in heaven, and forgive the sin of Thy people Israel, and bring them again unto the land which Thou gavest unto their fathers. When heaven is shut up, and there is no rain, because they have sinned against Thee; if they pray toward this place, and confess Thy name, and turn from their sin, when Thou afflictest them: Then hear Thou in heaven, and forgive the sin of Thy servants, and of Thy people Israel, that Thou teach them the good way wherein they should walk, and give rain upon Thy land, which Thou hast given to Thy people for an inheritance" (1 Kg. 8:33-36; repeated in 2 Chron. 6:24-27).