From LawGuru Wiki
Bride price also known as bride wealth or a dower is an amount of money or property paid to the parents of a woman for the right to marry their daughter. (Compare dowry, which is paid to the parents of a man.) Or the payment is an exchange for the bride's family's loss of her labour and fertility within her kin group.
 History of the tradition
They are too craven to go to the house of her father Icarius, that he may himself set the bride-price for his daughter, and bestow her on whom he will, even on him who finds favour in his sight.
and the custom lasts into classical times, by which time it had been become token, less valuable than the bride's dowry.
The tradition of giving bride price is still practiced in many Asian countries although the amount changing hands is more a token amount to continue the traditional ritual then an actual price-tag attached to the bride-to-be for marriage.
In Chinese culture, an auspicious date is selected to 'Ti Qin' (literally meaning 'propose marriage'), where both families will meet to discuss the amount of the bride price demanded, among other things. A couple of weeks before the actual wedding, the ritual of 'Guo Da Li' (literally meaning 'performing the rites') takes place (on an auspicious date of course). The groom and a matchmaker will visit the bride's family bearing gifts like wedding cakes, sweetmeats and jewelry as well as the bride price. On the actual wedding day, the bride's family will return a portion of the bride price (sometimes in the form of dowry) as a goodwill gesture.
The practice of bride price also existed in India, where it was considered as a social evil and the subject of a movement to eradicate it in the early 20th Century. Unlike what happened in the case of dowry, this movement was largely successful.
In parts of Africa the validity of a traditional marriage ceremony depends on the payment of a bride price which can vary from a token amount to really exorbitant figures.
 Similar Traditions
A similar tradition is the Morgengabe of medieval Germans, paid by the groom or his family to the bride. Its purpose was to secure the bride for widowhood, loss of other means of survival or loss of other property. Together the Morgengabe and dowry worked to give a start in life to a young couple, and secure the bride's future. This German tradition was followed by most people in medieval and modern Europe (all Western Europe being an outcome of Migrations of Germanic peoples), and only in recent centuries have the dowry and Morgengabe disappeared from European law.
Mahr (Arabic) is a similar tradition in Islamic marriage. It is a gift given by the groom to the bride. But unlike a bride price, it is given directly to the bride and not to her father. Although the gift is often money, it can be anything agreed upon by bride and groom. The Persian equivalent is Mahrieh. Qur'an verse 4:4 mentions mahr.
 The tradition in art
A famous Telugu play "Kanyasulkam" (Bride Price) satirised the practice and the brahminical notions that kept it alive. Though the practice no longer exists in India, the play, and the movie based on it, are still extremely popular in Andhra Pradesh.