Active bribery refers to the offence committed by the person who promises or gives the bribe; as contrasted to 'passive bribery', which is the offence committed by the official who receives the bribe. Active bribery occurs on the supply side, passive bribery on the demand side.
In legal lingo (according to the Council of Europe's Criminal Law Convention on Corruption, for instance), active bribery of public officials is defined as the " the promising, offering or giving by any person, directly or indirectly, of any undue advantage ... for himself or herself or for anyone else, for him or her to act or refrain from acting in the exercise of his or her functions". Similarly, passive bribery is "the request or receipt..., directly or indirectly, of any undue advantage, for himself or herself or for anyone else, or the acceptance of an offer or a promise of such an advantage, to act or refrain from acting in the exercise of his or her functions".
It is important to note that "active bribery" does not always mean that the briber has taken the initiative. In fact, often the reverse is true. The individual who receives the bribe often demanded it in the first place. In a sense, then, he or she is the more "active" party in the transaction.