What are we to understand by the bruised reed and smoldering wick in
Matthew 12:20? “A bruised reed he will not break, and a smoldering wick he will not snuff out, till he has brought justice through to victory.”

This language is no doubt figurative. What is it that these two expressions mean?

The simplest explanation seems to be, that the Holy Spirit is here describing persons whose grace is at present weak, whose repentance is feeble, and whose faith is small. Towards such persons the Lord Jesus Christ will be very tender and compassionate.
Weak as the bruised reed is, it shall not be broken;
small as the spark of fire may be within the smoldering wick,
it shall not be quenched.
– J.C. Ryle (1816-1900)