Asura Marriage is when a unsuitable bridegroom approaches the family of the bride and offers a high `price` to get married to the girl. It could be looked upon as bribe for getting the girl the boy desires even if he is in no way is a match for the girl. So the system of marriage is more like buying a product. This form of marriage is more popular amongst low caste Hindus. This kind of marriage is common among the tribes in India.
While performing holy yajna marriage is performed and the parents of girl give some dowry to bridegroom. It is not blessed by learned persons due to the involvement of dowry system, etc.