At this Bible Student website, they discuss it in CTR's biography.
http://www.heraldmag.org/olb/bio%20ctr.htm
HIS DYING HOURS
A few weeks ago he started on a trip to the Pacific Coast, preaching every evening, and traveling throughout the remainder of the night and of the day. His last sermon he preached to the Congregation at Los Angeles; and being too weak to stand, he sat throughout the discourse. He left Los Angeles Sunday evening on his return to Brooklyn, and rapidly grew weaker. Seven hours before his death, addressing his traveling companion, Brother Menta Sturgeon, he said, "Make me a Roman toga."
Using the bed sheets, Brother Sturgeon made a toga, which Brother Russell put on himself. He stood erect for a moment, and then lying down on the couch in his Pullman drawing room, closed his eyes, thus in symbolic language speaking of death. A great deal of the Bible is written in symbolic language, and it was quite appropriate that he should speak his last message in symbols. It is interesting here to know what a Roman toga symbolizes: Augustus’ Poet Laureate, said, "It is by the toga that the royal nation is recognized." The word toga means a covering garment (white robe). It was the official robe of higher magistrates, priests and of persons discharging vows, and was worn on special occasions, such as celebrating a triumph.
We are reminded of the last experiences of the Apostle Paul, who traveled with his beloved companion Timothy, whom he called his son-not a natural son, but, as St. Paul stated, he had begotten this young man in the spirit. Likewise Pastor Russell begot Brother Sturgeon in the spirit, in that he brought Brother Sturgeon to a knowledge of the divine plan. Shortly before St. Paul’s death he wrote, "I am now ready to be offered up, and the time of my departure is at hand; I have fought a good fight, I have finished my course, I have kept the faith; henceforth there is laid up for me a Crown of Righteousness, which the Lord, the Righteous Judge, shall give me at that day; and not to me only, but unto all them also that love his appearing." (2Ti 4:6-8) Our dear Brother Russell not only loved the appearing of the Lord Jesus, but above all men on the earth he declared the presence of the Master. Brother Russell was a very modest man and never exalted himself. It was exceedingly difficult to get him to speak of himself.
He chose, therefore, a symbol which we could afterwards interpret to speak practically the same thing spoken by the Apostle Paul. By wearing the toga Brother Russell in effect said, "I have fought the good fight; I have triumphed and shall be received as a member of the royal family of heaven."