The British colonists, upon observing the similarities of this custom to their own, applied the English term "dowry" to it. The practice, while largely extinct in mainstream British society, has held on in parts in South Asia (though many modern South Asians consider it abhorrent), and therefore its modern colloquial use is more connected to the South Asian custom.
There is a separate practice of the bride's parents gifting her with items of jewelry which are intended to be her sole property - a sort of insurance policy against an unreliable husband - and not that of the groom or his family. Whether that was honored or not obviously depended a lot on the situation. This practice has actually continued relatively unabated, and it is partially responsible for the high demand for gold in South Asia during wedding seasons.
Pedant here. Hello everybody!
There is a difference between dowry and bride price. Traditionally the dowry in culture with custom of primogeniture was the portion of inheritance the bride brought with her. It's a bribe to the groom's family not to contest the rest of the inheritance when his father-in-law dies, not to put a fine point on it.
Following Anglo-Saxon customs (which was heavily influenced by the Vikings) brides were given morgangifu, literally morning gift, from her husband the morning after the wedding. This is hers to take with her and her children, after a divorce or death of the husband. See also morganastic marriage, where a woman and her children get nothing except the morning gift, that is, she and the kids don't get the traditional inheritance (crown, title, land, such). It's a payoff to the bride's family to not contest what's regarded as the groom's family's property, not to put a fine point on it.
The bride price is the cost paid by the groom to the bride's family, this practice was more common in Asia and the tribal Middle East. Women were regarded as property, her leaving the family home and joining the family of her husband is regarded as a loss to her clan. In ancient Chinese text, lesser wives not just concubines were bought, literally.