This theory is based on the studies of chemists Johannes Nicolaus Bronsted and Thomas Martin Lowry.
Together they defined acid and base in the absence of water, which is not explained by Arrhenius's theory. The theory is based on giving or receiving 1 proton.
Bronsted-Lowry Acid - is the whole chemical species that donates 1 proton.
Bronsted-Lowry Base - is every chemical species that gets 1 proton.
In this case, HCl donates 1 proton to ammonia (NH3). In the reverse reaction, NH4+ is the one who donates 1 proton to Cl- ion.
Bronsted-Lowry acids and bases form conjugate pairs. Always an acid and a base. The acid of the first reaction and the base it formed. Like this:
HCl and Cl- are conjugated pairs.
HCl is the conjugate acid of its conjugate base Cl-.
NH3 and NH4+ are conjugate pairs.
NH3 is the conjugate base of your NH conjugate acid4+.