Dakshina is typically used to mean an offering. "Daksha" means "capable". Dakshina means what is given out of one's capability and willingness.
The word Dakshina begins with the syllable 'Da,' with which Prajapathi prescribed three sets of sons (the devatas, the asuras, and ordinary men).
The three not only his sons, but also disciples. At the completion of their studies, they asked him for a guiding mantra. Prajapati smiled and asked each to approach him separately. Into each son's ear, he uttered the syllable 'Da'.
Due to their differing qualities, each heard something different for the beej mantra
- the devatas heard "DA" meaning continence (self-restraint)
- men heard "Daan" meaning to give
- and the asuras heard "Daya" meaning compassion
Dakshinamurty, a form of Siva, is called so because He gives the knowledge of unalloyed Truth, and the ability to differentiate apparent from real.