Here's what's going on here.
The ammonium cation,
Now, this proton is being added to the ammonia molecule, to the central nitrogen atom, to be precise, via a dative covalent bond, sometimes called a co-ordinate bond.
What that means is that the lone pair of electrons present on the nitrogen in the ammonia molecule now acts as a pair of bonding electrons between the nitrogen atom and the added proton.
In other words, nitrogen shares the lone pair of electrons it has in ammonia with the incoming proton. These electrons will now act as bonding electrons and will keep the hydrogen atom bonded to the nitrogen atom.
The incoming proton carries a
So, to sum this up, the two electrons that make up nitrogen's lone pair in ammonia are now being shared with the incoming hydrogen atom, i.e. they are involved in a dative covalent bond.