The bishop, and others in comparable positions, can forgive in the sense of waiving the penalties. In our loose connotation we sometimes call this forgiveness, but it is not forgiveness in the sense of ‘wiping out’ or absolution.
The waiver means, however, that the individual will not need to be tried again for the same error, and that he may become active and have fellowship with the people of the Church. In receiving the confession and waiving the penalties the bishop is representing the Lord. He helps to carry the burden, relieves the transgressor’s strain and tension, and assures to him a continuation of Church activity.
It is the Lord, however, who forgives sin.
(Spencer W. Kimball, The Miracle of Forgiveness, p. 332)