The phrase describes two different things depending on who is saying it. As a provision idea it means each identified risk gets an extinguisher suited to it. As an operational idea it means one person, one fire, one extinguisher: if the first unit does not deal with it, the answer is to leave rather than to fetch a second. Both readings are sound and they belong in different documents.
The fire point
Extinguishers are normally grouped at fire points rather than spread singly, so that a person learns one location per area rather than many. A fire point carries the units appropriate to the risks reachable from it, a sign identifying it, and often the call point. Grouping also makes the monthly check tractable, because there is a finite list of places to visit.
Why the second extinguisher is usually the wrong decision
A portable unit discharges in seconds. If a fire has survived one correctly chosen unit applied correctly, it has grown past what portables address, and the time spent fetching another is time not spent leaving. Training that says try once and then go produces better outcomes than training that implies persistence.
Matching the unit to the risk rather than the room
A fire point outside a kitchen holds wet chemical because the kitchen is what it serves. A fire point by a switch room holds carbon dioxide. A fire point in a corridor of offices holds class A cover. The provision follows what is behind the doors, which is why the assessment has to be room by room.
What the fire risk assessment records
The location of each point, what it holds, and which risk it serves. That record is what makes the monthly check meaningful and what allows an enforcing officer to follow the reasoning rather than simply count cylinders against a floor area.
Questions people ask about one fire one extinguisher
Does each fire risk need its own extinguisher?
Each identified risk needs an agent rated for it within reach. One unit can serve several risks where its rating covers them all, which is common for class A.
Should somebody use a second extinguisher if the first fails?
Generally no. The instruction in most training is one attempt and then evacuate, because the fire has demonstrated it is beyond a portable.
Is a fire point a legal requirement?
The law asks for appropriate fire fighting equipment, easily accessible, simple to use and indicated by signs. The fire point is the ordinary way of satisfying all four at once.