We may understand this to refer to justification. "They shall walk in white"; that is, they shall enjoy a constant sense of their own justification by faith; they shall understand that the righteousness of Christ is imputed to them, that they have 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 have not defiled their garments shall have their faces always bright; they shall understand what Solomon meant when he said "Go thy way, eat thy bread with joy, and drink thy wine with a merry heart. Let thy garments be always white, for God hath accepted thy works." He who is 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 is because so many believers defile their garments with sin and error, and hence they lose the joy of their salvation, and the comfortable fellowship of the Lord Jesus, they do not here below walk in white.
The promise also refers to walking in white before the throne of God. Those who have not 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 knoweth not, blessedness which even the stretch of desire hath not 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.