When Sri Sita Devi was imprisoned by Ravana in The Asohka Vanam, Sri Hanuman went there and bowed to Sita Devi. Sita Devi, who is an embodiment of Goddess Maha Lakshmi was sitting amidst the betel leaf vine. When Lord Hanuman announced himelf as the messenger of Lord Rama and sought Her blessings, Sita Devi became overjoyed and blessed Lord Hanuman with betel leaves she plucked from the vine.
The tradition of adorning Lord Hanuman with Betel leaves honors that incident and pleases Lord Hanuman and through Him Goddess Sita Devi, thereby bringing prosperity to the devotee.