"Let us hold fast the confession of our hope without wavering, for He who promised is faithful" (Heb 10:23). The Greek word for confession means to say the same thing or to agree with. Another way to look at it is to speak out of as with a public declaration. Since it is confessing your hope it is agreeing with the expectation which you have identified. That is what you "hold fast . . . without wavering" (:23). Your faith depends on that "He who promised is faithful" (:23). "The promise was approaching which God had assured Abraham" (Ac 7:17). But make sure you aren't a "double-minded man, unstable in all his ways" (Ja 1:8). If you waver you're not holding fast and you can drift away. The most important aspect of this is when "you confess with your mouth Jesus as Lord" (Ro 10:9). There's a saying that you should put your mind in motion before setting your mouth in gear. But with the engine running in neutral you'll never get anywhere if you don't engage the transmission. So when you "believe in your heart that God raised Him from the dead, you will be saved" (:9) and "with the mouth he confesses, resulting in salvation" (:10). The first part of the verse says "with the heart a person believes, resulting in righteousness" (:10). Its as if without the second half of the verse the process is incomplete. Some have pointed out that even though doctrine itself is truth, if its only treated mentally, it isn't alive and has to be activated before it can be used.
Jesus said that "'everyone who confesses Me before men, I will also confess him before My father who is in heaven'" (Mt 10:32) and "'also before the angels of God'" (Lk 12:8). Its as if it was a requirement to speak it out openly "before men" (Mt 10:32). But the Pharisees said "if anyone confessed Him to be Christ, he was to be put out of the synagogue" (Jn 9:22) so "they were not confessing him" (12:42). Paul advised to "fight the good fight of faith; take hold of the eternal life to which you were called" (1Ti 6:12). He recognized that "you made the good confession in the presence of many witnesses" (:12). So as "partakers of a heavenly calling, consider Jesus" (Heb 3:1) who is the "great high priest who has passed through the heavens" (4:14) and the "High Priest of our confession" (3:1).
The author of Hebrews warns to hold on to the "confession of our hope" (Heb 10:23). Should the word's use be limited to just declaring, agreeing and praising? Or should its understanding be expanded to the larger context to where it is also used? If it means to audibly profess before men then when they were baptized in the Jordan River "they confessed their sins" (Mt 3:6) applies. Doctrinally "if we confess our sins He is faithful and righteous to forgive us our sins" (1Jn 1:9). The big picture is "your obedience to your confession of the gospel of Christ" (2Co 9:13). "The one who confesses the Son has the Father also" (1Jn 2:23) and "whoever confesses that Jesus is the Son of God, God abides in him, and he in God" (4:15). "Every tongue will confess that Jesus Christ is Lord" (Php 2:11) and "every spirit that confesses that Jesus Christ has come in the flesh is from God" (1Jn 4:2). In the longer perspective "all these died in faith, without receiving the promises, but having seen them and having welcomed them from a distance" (Heb 11:13). They had "confessed that they were strangers and exiles on the earth" (:13).