'Swaha'-The union of my light with the divine light. The union of the self and the divine. Aham Om Asmi.

Svaha is one of the very important words which is almost always uttered while making offerings in the fire (or to Agni). Usually, it (Svaha) is understood to mean "I offer this oblation to you (i.e. Brahman -- in the form of Agni)".

Veda indicates something different also as the meaning of Svaha -- 'Let my light (soul or self) be in union with your (i.e. Brahman's) Light (Self)'. Thus the uttering of Svaha during yajna while making offerings into the fire really is the invocation of that union (relationship) between the devotee (worshipper) and his / her Lord.