The right to counsel was one's right to seek and be represented by a lawyer or other legal advisor of their choosing.
In 2267, Captain James T. Kirk advised Spock of his right to counsel at a hearing into his apparently mutinous diversion of the USS Enterprise on Christopher Pike's behalf. Spock waived that right and demanded the hearing be cancelled in favor of a court martial. (TOS: "The Menagerie, Part I")
In 2372, wishing to commit suicide, Quinn noted he had a right to counsel and asked for Tuvok's aid. (VOY: "Death Wish")