Supplication (noun) is the act of making a humble, earnest petition, a formal form of begging. A supplicant (noun) is one who takes a kneeling position before an authority to petition. To supplicate (verb) is to kneel and bow one's head.
Supplication and spanking
In consensual spanking, the submissive may have feelings of remorse and assume a penitent position. This means he/she kneels and bows the head as in a ritual. The spanker listens to the confession, then announces what the punishment will consist of, e.g. number of strokes, corner time, extra chores.
In the knees-and-chest position, the bottom's buttocks are high in the air with the head and shoulders bowed down as a supplicant. The spankee is undressed and may place the arms out in a forward manner. The on-all-fours position is similar in that the spankee must kneel to present the naked buttocks, but relies on the elbows for support. In supplicant positions, often the knees are spread to present a man's scrotum or woman's labia.
A session may start in an improptu manner, e.g. a confession to the dominant that the bottom has broken a rule. The submissive seeks foregiveness and asks to be punished. The scene then unfolds as the Master or Mistress orders the spankee to prepare him or herself, which may be entailing placing oneself over the dominant's thighs or going to the bedroom, undressing and assuming to required spanking position.
There is an element of humiliation in such supplication as it may expose the buttocks, labia or scrotum, and anus to punishment. With the bottom's head bowed, the spanker has complete control of the scene. By agreement, the spanker may leave marks as a sign of domestic discipline. In the aftermath, such marks may be displayed by the bottom. Once the punishment is complete, foregiveness is granted.