We may understand this to refer to being made right with God. "They shall walk in white;" that's, they shall enjoy a constant sense of their own being made right with God by faith; they shall understand that the righteousness of Christ is imputed to them, that they've all been washed and made whiter than the newly-fallen snow. Again, it refers to joy and gladness: for white robes were holiday dresses among the Jews. They who haven't defiled their garments shall have their faces always bright.
They shall understand what Solomon meant when he said "Go your way, eat your bread with joy, and drink your wine with a merry heart. Let your garments be always white, for God has accepted your works." He who's accepted of God shall wear white garments of joy and gladness, while he walks in sweet communion with the Lord Jesus. Whence so many doubts, so much misery, and mourning? It's because so many believers defile their garments with sin and error, and so they lose the joy of their salvation, and the comfortable fellowship of the Lord Jesus, they don't here below walk in white.
The promise also refers to walking in white before the throne of God. Those who haven't defiled their garments here shall most certainly walk in white up yonder, where the white-robed hosts sing perpetual hallelujahs to the Most High. They shall possess joys inconceivable, happiness beyond a dream, bliss which imagination knows not, blessedness which even the stretch of desire hasn't reached. The "undefiled in the way" shall have all this—not of merit, nor of works, but of grace. They shall walk with Christ in white, for he has made them "worthy." In his sweet company they shall drink of the living fountains of waters.
Closing Prayer
God, as we start this day, help us trust You fully, even when the path isn't clear. We pray in Jesus' name, Amen.