# For Zion's sake I will not be silent, and for Jerusalem's sake I will not be quiet

"For the sake of the people of Jerusalem I will not be silent" 

# I will not be silent

It is most likely that "I" refers to Isaiah.

# until her righteousness proceeds brightly, and her salvation as a burning torch

Both clauses reassure the people that God will eventually come and save the people of Israel and that it will be as apparent as light is.