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Many times I've banged my poor overworked, under performing head at both virtual and physical walls trying to understand why do we have the object scale attributes when every time we want to apply a modifier or perform some operation the object scale has to be exactly one in all three directions if we don't want our result to look like creations from other dimensions:
How is this feature useful and why is it still in Blender?
Here is how it really is under Blender's hood:
So if you scale a cube into a block, the mesh is still a cube but the object is a block. You can have the same cube mesh linked in many objects, each being a different block.
When you apply the scale (or any other transform) you make the mesh actually reflect the transformation. This change would project into all other objects with this linked mesh.
Some Blender operations only operate on mesh and don't take object transformations into consideration - like UV unwrap for example. That's why scale needs to be applied.
The confusion is imho Blender's fault. In edit mode it should actually display what the mesh really looks like (like it does with modifiers), or these operations should be written properly to account for object transforms - so what you see is what you get - a thing every gui and program should follow..
Additionally to the above answer Scaling doesn't necessarily need to be always applied, most modifiers work well with it, although common problems stem from non applied or non uniform scale.
It is however a valid transformation method, even if temporary, and is also often useful for animations, like stretching effects, growing poping up, etc..
Correctly used it can save a lot of resources by using scaled instances of the same cloned objects, instead of having different meshes just for different sizes
I'm not sure if this will answer your question, but I'll give it a try.
You can scale your objects using either the "Scale" fields, or the "Dimensions" fields:
While you can give your object exact dimensions using the "Dimensions" fields, you can alternatively use the "Scale" fields to, say, reduce or increase your object's size by a given %.
Let's say I want to stretch Suzanne's head (whose dimensions on x,y,z are: 2.734, 1.703 and 1.969 respectively) a 25% on the z-axis. What I'll do is grab the z field inside of "Scale" and change it from 1.00 to 1.25:
X and Y dimensions remained the same, but the Z dimension increased by a 25% with respect its old value. Now I simply go to Object > Apply > Scale to tell Blender: "Hey buddy, these dimensions will be considered from now on as the default dimensions upon which I'll be working on. Take them as the REFERENCE for subsequent operations":
How would I increase the Z-dimension by a 25% without the "Scale" field? I would need to type inside of the Z-field inside of "Dimensions" the following: 1.969+0.25*1.969
So, the "Scale" fields are there for pure mathematical convenience, as far as I know.
