What is meant by it? That's a good question...
Well, as an outward show of deep sorrow in the Hebrew culture, they used to wear these scratchy, itchy garments made out of rough material or animal hair, called a CILICE. The word is pronounced SILL-iss, and this is also called SACKCLOTH. It was meant to be an outward symbol of deep humility--- like wearing a public sign that said,

"YES I BLEW IT, I AM AN IDIOT, FORGIVE ME."

"And it came to pass, when Ahab heard those words, that he rent his clothes, and put sackcloth upon his flesh, and fasted, and lay in sackcloth, and went softly. And the word of the LORD came to Elijah the Tishbite, saying, Seest thou how Ahab humbleth himself before me? because he humbleth himself before me, I will not bring the evil in his days: but in his son's days will I bring the evil upon his house." - 1 Kings 21:27-29

Sometimes entire groups and communities would wear these garments to show despair and sorrow... in this case, it would be like everyone wearing signs that said,

"WE ARE VERY UPSET AND IN MOURNING."

"When Mordecai perceived all that was done, Mordecai rent his clothes, and put on sackcloth with ashes, and went out into the midst of the city, and cried with a loud and a bitter cry. And came even before the king's gate: for none might enter into the king's gate clothed with sackcloth. And in every province, whithersoever the king's commandment and his decree came, there was great mourning among the Jews, and fasting, and weeping, and wailing; and many lay in sackcloth and ashes." Esth. 4:1

Fredoheaven; I think if you did that in public in our culture here today people would simply think you were strange and you might cause harm to the cause of Christ because people might think you a lunatic. On the other hand, if you were very upset about something you did and wanted to wear itchy clothes in private, hey go for it---I'm not going to criticize you for it. Personally, I prefer to simply pray and seek forgiveness, now that we have an advocate with the Father...

"My little children, these things write I unto you, that ye sin not. And if any man sin, we have an advocate with the Father, Jesus Christ the righteous: And he is the propitiation for our sins: and not for ours only, but also for the sins of the whole world." - 1 John 2:1-2

"Let us therefore come boldly unto the throne of grace, that we may obtain mercy, and find grace to help in time of need." Heb. 4:16

Strange but true; some Catholics down through the ages (Opus Dei) have taken this self-punishment to a whole new level (mortification) by wearing a METAL CILICE, with nasty little spikes on the inside to cause extra discomfort and pain for themselves. Ouch.