What does the neutralisation of acids and bases mean? From what I found in textbooks and google is that neutralisation is when acids and bases react to produce salt and water. Most examples I have learnt do so, however a reaction like: 

$$\ce{NH3 + HCl -&gt; NH4Cl }$$

It does not produce water.

So is neutralisation defined as only when salt and water produce a neutral salt and water or is it just produce any salt and water. And if it is any then how can does the example above work?
There are many theories put forward to explain acid-base reaction.
According to Arrhenius acid-base theory. All acid liberate protons (H+ ions) when dissolved in water. All bases liberate Hydroxyl ions (OH- ions) in water.
When the reaction takes place H+ and OH- combine to form water, and the remainder of the ions (what are left after liberating H+ and OH- ions) form what is called a salt.
In such reactions, Water is always formed.

What you have shown is an example of a Bronsted acid-base reaction.
Bronsted acids are proton donors (have ionisable hydrogen ion).
Bronsted bases have the capability to accept them (either via hydroxyl ion liberation or by their lone-pair as in NH3)

Clearly, the formation of water is not a necessity in a Bronsted acid-base reaction.