what is a scale?

A scale is a theoretical construct.

Yes, I am saying that it's not actually a musical thing. It's an extra-musical thing. It's an idea that people came up with to try to explain certain qualities and phenomena that happen in a body of performed music, that is, a repertoire. Those people lived in ancient Greece a long, long time ago and were writing about their music.  

Specifically, in the late 5^th & early 6^th centuries (CE), Roman philosopher Boethius translated writings by Nicomachus (who lived in the 1^st century CE) for the education of a particular noble woman and provided his own commentary. Nicomachus' ideas were based on the writings of Pythagoras, who lived five hundred years before Nicomachus. All of these people were of a specific socio-economic class and their ideas are based partly in practice and partly in a philosophical-mathematical-mystical-religious world view.¹

The writings of the ancient Greeks about their ancient music was considered by the scholars in the Middle Ages to be so logical and neatly presented that it must be universally true. Boethius and those who followed proceeded to try to reconcile these theoretical writings with their own actual practice, with mixed results. Long story short, many terms stuck even though the logical beauty and sense of the ancient Greek writings never really applied. However, the idea of intervals and pitch collections was something that was phenomenologically true, and was applied to European musics, even if the nomenclature got a little garbled.

All of that said, the whole point of theory is that it's supposed to be a helpful way to conceptualize music, so that you can make music more sensitively, even though sometimes the theory is convoluted and complex. In short, scales are a useful thing to understand and apply in one's practice.

Now you might be saying, Andrea, I see and hear scales in music all the time. And it's true, you'll see and hear a complete scale in the wild, but make no mistake: the music came first. Parts of melodies sometimes come in the form of a scale, but most melodies are not simply iterations of scales up and down. A scale (or mode!) is simply an inventory of structurally important pitches used in a piece of music (melody AND harmony), put in stepwise order, starting and ending with the tonic. "Structurally important" means that there might be some pitches that are not structurally important, they are simply ornamental.² 

What's fascinating is that even without being able to name this phenomenon, your brain figures it out — even when you are a baby. But we know what pitches are and are not structurally important, not because there's an existing scale that tells us so, but because of the melodies themselves (and harmonies — but even without accompaniment, we can usually figure out the resting tone). "Starting and ending with the tonic" automatically emphasizes that pitch. Yet again, it's the music that comes first — our brain also figures out which pitch is the tonic, the most important pitch in the structure, even as babies. 

What is the difference between a scale and a mode? In one sense, nothing: they are both collections of pitches put in stepwise order. In medieval times in Europe, modes came in two forms: one with the tonic (or "resting tone") at the beginning and one with the resting tone in the middle. Now, we call that the tessitura — the range of the melody, but we put our pitch sets — the scale or mode — always with the tonic first, regardless of what range the melody actually encompasses. In modern theory, a scale implies that we have a piece of music in which there is a "traditional" (that is, Classical Music) dominant chord that signifies a return to the tonic — a major tonality based around a major scale, or a minor tonality based around the three types of minor scales so that you have that kind of dominant chord. Anything with a different signifying chord ("incoming") would be considered a mode.

Again, in practice, we are actually talking about melodic shapes that are doing the signifying. Even though, say, Mozart, Ellington, and whoever is writing BTS' material are all writing modern, tonal music which could be reduced to a basic structural scale, we can hear that the melodic shapes that make are different from one another. That is, how the melodies that Mozart, Ellington, BTS, American Folksong, Czech Folksong, etc. create signify what the resting tone is — those shapes are different. Those melodic formulae are partly idiosyncratic and partly informed by the culture they are in. A mere scale won't tell you much about how to make those melodies, in the same way that just having a scaffold will only tell you so much about the resulting architecture.

If you are looking for a reason to avoid practicing scales, I can give you one: Even better than practicing scales is to learn a lot melodies in all transpositions, throughout the range of your instrument. This will develop your ear-instrument relationship and sense of melodic style better than anything else. There's one catch, though. It's much easier to do these transpositions when you know all your scales.

1. I suppose you could say this about all music theory — partly practice, partly value-system.

2. Alternately, in more complex pieces, there are pitches whose job it is to signal that we are moving to a new pitch collection