Walk of atonement

"A sinner comes before you, Cersei of House Lannister. Mother to His Grace, King Tommen, widow of His Grace, King Robert. She has committed the acts of falsehood and fornication. She has confessed her sins, and begged for forgiveness. To demonstrate her repentance, she will cast aside all pride, all artifice, and present herself as the gods made her... to you, the good people of this city. She comes before you with a solemn heart, shorn of secrets, naked before the eyes of gods and men, to make her walk of atonement."

- The High Sparrow to the people of King's Landing

A walk of atonement is a public ritual of punishment and penance in the Faith of the Seven. It demands a confessed sinner to walk a certain distance stripped of all clothing, exposed to the eyes and jeers of the population.

Season 5
After being caught at a brothel in the middle of a session of blasphemous sexual roleplay, the High Septon is trapped by a group of Sparrows, stripped of all his clothes and forced to walk naked through the streets of King's Landing, while one of the Sparrows publicly names him a sinner and beats his hands to keep him from covering his genitalia.

After a time imprisoned by the Faith of the Seven, Queen Cersei confesses to having committed adultery with her cousin Ser Lancel Lannister, who had joined the Faith Militant and accused her of fornication, regicide, and incest. The High Sparrow reveals she will still be tried for the two other charges she denies while allowing her to return to the Red Keep only if she performs a walk of atonement as penance for her confessed sin. Cersei's hair is cut short and then she's presented to the population of King's Landing so they will bear witness to her confession and penitence. She's stripped of her clothing and made to walk from the Great Sept of Baelor to the Red Keep, escorted by members of the Faith Militant, who keep away the leering and jeering crowds who have gathered to see her shame and take the chance to insult a Queen. As she walks, Septa Unella accompanies her crying out "Shame!" repeatedly while ringing a bell to attract the attention of the population.

In the books
In the A Song of Ice and Fire novels, it seems walks of atonement are civil punishments reserved to publicly shame women accused of adultery or whoring. It also serves as a means of degrading these woman and stripping them of whatever pride or power they might hold.

Tywin Lannister forced his father's mistress into a walk of atonement after Lord Tytos died. While it is common for widowed lords to take lowborn women as bedwarmers, Tytos's mistress had come to dominate him utterly, being seated beside him beside him in the hall, showered with gifts and honors, even being asked her views on matters of state. She came to steal from him, order the household knights about, dismiss servants and help herself to the jewelry of the late Lady Jeyne, Tytos's wife. She grew so influential that it was said about Lannisport that any man who wished for his petition to be heard should kneel before her and speak loudly to her lap, for Lord Tytos's ear was between his lady's legs.

Lord Tytos died of a heart attack while climbing stairs to see her. The first thing Tywin did on his return from King's Landing was to expel the mistress from Casterly Rock. All the self-seekers who had named themselves her friends and cultivated her favor abandoned her. The silks and velvets Tytos had lavished on her and the jewelry she had taken for herself was stripped from her. Tywin had her stripped and sent forth naked to walk through the streets of Lannisport to the docks, telling everyone she met in the way she was a thief and a whore. Though no man laid a hand on her, that walk spelled the end of her power.