Lewis concept provides us with the concept of acid as the acceptor of electrons.

And this criterion for acid to be an acceptor it has to have 2 properties i. It should have a positive charge or ii. It has to have some electron deficiency to accept new electrons.

For the molecule of BF₃, it is short of an octet of electrons the central atom B has 6 electrons and is electron deficient hence, acts as a good lewis acid to fulfil its valence shell octet in spite of having no protons.

Therefore, it readily accepts lone pair of electrons from NH₃ and reacts with it.