Given a roughly flat surface, we need to turn it into one that is completely flat. The quality of the finish does not matter at this stage, the important thing is that the broad shape of the surface is a flat plane without curves, hollows or ridges. So "Flat" is being used in a particular way here. We are not saying that the surface will be nice and smooth - it wont - but we are saying that the surface we create will define a single plane over the wall surface that hasnt got any major curves, bends, hollows or bumps on it - it will be globally "flat", though not "smooth".
Later we will put a thin coat of fine material over it to get the finish. That coat will be uniformly thin and wont be able to correct any major geometric faults; it will just put a good surface onto something that is already flat. If we cannot make the surface flat in the first place then the thin finishing coat will not fix it later.
So how do we get this flat plane? how do we define this flat surface?
The traditional way is called "plumb dot and screed".
At one end of the wall we stick two small pieces of flat wood (thin ply) on some blobs of plaster; one near the top of the wall, and one near the bottom. These are the "Dots".
We then use a straight edge and spirit level to align these two bits of wood vertically, so they are "plumb" (as in "plumb-line"). Then we do the same at the other end of the wall. So at each end the pair of dots defines a straight vertical line, and the four dots as a whole define the surface we will create.
These two verticals might be at slightly different distances from the wall, and we use some judgement to decide how far to set the first dot in each pair from the wall surface. If we were badly out then one wall would not form a 90 degree angle to its neighbour, and we might also use a lot more plaster in creating the surface. But we are unlikely to be far out unless we do something quite extreme.
The picture below shows three pairs of dots set up. I will explain why this wall has three pairs later, and how to set the intermediates so they are on the same plane; you only need that for long walls. In this case a base coat of plaster was also applied to the wall to get it more roughly flat in the first place and build it up a bit where the hollows were bad.
With the dots in place we can form a horizontal bar (Screed) between them by filling the horizontal gaps with bonding plaster, then using a long ruler horizontally to rule off surplus material between the dots. The whole bar (screed) will then be at the same height as the dots.
The screeds give us two horizontal rails which we can use to 'rule-off' the rest of the wall.
What if your wall is too long for your ruler to reach between the dots when you are ruling off the screeds? Then make intermediate dots so the distances between dots is ok for the rule edge. These intermediate dots need to be on the plane too, so care is needed. You could stretch a piece of string between the end dots and get your intermediates to the right height that way. I perfer a laser because its beam will definitely be straight all the time. String might be being pushed out a little by the intermediate dots.
More plaster can now be applied to the rest of the wall, and we use a long ruler vertically, running it along the screeds to scrape off surplus material. When we can do that and see the ruler just touches the wall everywhere, we have the flat plane we desire.
Next the plaster needs to gel until it starts to become quite firm. At this point we can take a solid trowel - made of wood or polyurethane - and 'scrub' the surface gently. We are not trying to change the basic flatness of the surface in any way, but because this 'float'ing trowel does not bend it will tend to scrape off parts that are slightly proud, and such surplus material that is generated that way will fill in any slight hollows. So the intention is to improve the flatness of the surface, rather than to destroy it. That bit seems to take the most practice to me, and the timing is important. Do it too soon and its like trying to polish porridge; too late and its like trying to iron stone. But then, most of plastering is about getting these 'timings' right.
Because of this "float"ing action to get the flatness - and I suppose you could regard the ruling across the screeds as a kind of 'floating' the ruler across the screeds, taking off surplus flaster to define a flat surface - this whole coat is called the 'floating' coat.
The overall purpose then of the whole plumb-dot and screed, floating coat game, is to get our flat plane. Given this flat surface, the next step is to put a fine surface on it.