Actually, the adduct is formed due to co ordinate covalent bonding between the boron trifluoride and ammonia.
It is because, the boron trifluoride is a lewis acid having tendency to gain an electron pair and ammonia is a lewis base which has tendency to donate a lone pair and so, the ammonia donates its lone pair to BF3 there by creating the co-ordinate bond . The arrow hence, points towards BF3.
As: NH3->BF3
It is called as adduct because, there is no loss of atoms in the formation of the compound and the compound is formed by covalent co-ordinate bond.
Here, the coordinate bond is formed because the reacting species do not bear any charge.