ANSWER - Athena is a Goddess of the Greek pantheon associated with wisdom and justice. Her wisdom is symbolised by her association with the owl and her Roman counterpart is Minerva.Some Pagans and Witches either do not believe in deity at all or consolidate their idea of deity into a dual idea of God and Goddess (most usually Wiccans). For those who do believe in different deities of a specific pantheon, to be favoured by a God or Goddess is to gain their support and their protection. The support offered will be in the character and spirit of the deity from which it is offered, so for example, to be favoured by Morrigan the Celtic Goddess of War you may receive support in conflict but to be favoured by Hestia, the Goddess of the hearth may be to receive blessings for your home and your family.
In the specific case of Athena I would imagine her favours would take the shape of bringing success to you in intellectual endeavours, possibly in academic studies or a difficult project at work. Athena is also associated with precision, logic and justice so being favoured by her may mean strategic assistance in situations that need a logical structured approach.
Beliefs vary, some of those who worship specific deities believe the deity will intervene on their behalf in the world. Others believe it is the individual’s own soul/mind that is assisted by the deity.