(What they mean is that the descriptions of language which are called 'grammar' are helpful. The other meaning of grammar is 'the process by which we stick words together to make meaning'. That precedes the terms that people have come up with to describe the process. In the history of the human race, people used language before they came up with terms to describe what they were doing. So there are two meanings (at least!) for the word 'grammar')
Anyway, are the descriptions that children have to learn, 'helpful'?
Here is the Cambridge Grammar's definition of a 'subordinate clause':
Let's leave to one side the fact that old school purists wouldn't allow for that 'finite' OR 'non-finite' thing, so the dogmatic statement, 'They can be...' has to be qualified by 'on the other hand, plenty of old school purists would say they can't.' (I don't care either way.)
Now for the definition itself.
The word 'dependent' is a description of a group of words (a clause) that can only be deduced from meaning. How else can they decide that something is 'dependent' or not?
And that, let's remember, is the defining characteristic of this particular 'clause'.
Look at the sentence 'She had pretty hair and must have been nice-looking when she was young.'
Yes, it's clear that 'when she was young' entirely on its own is incomplete if you pull it out of this sentence and leave it on the page. In real life, of course we often say things like 'When she was young' because we're answering questions for which that's the answer and you can say in that case, it was 'dependent' on the question.
So, the idea is to become complete, 'when she was young' 'depends on' what came first in that sentence: 'She had pretty hair and must have been nice-looking...'
Now, let's look at that first part of the sentence which is supposed to be 'independent' or 'main': "She had pretty hair and must have been nice-looking."
Remember that these structures are derived from meaning and then abstracted into something 'structural' ie 'clauses' and 'types of clauses'. Can we really say that 'She had pretty hair and must have been nice-looking...' is really 'independent'? The whole point of the sentence as a whole revolves round a state the person is in at a particular point in time. The whole meaning and purpose of the so-called 'independent clause' depends on the so-called 'dependent' (or 'subordinate' clause), otherwise there would be no point in writing it. In other words the so-called 'independent clause' depends on the so-called 'dependent clause' when we consider the sentence in relation to its meaning and any possible function it might have in a passage of writing. So we have a terminology that was derived from meaning, was turned into a structural rule, yet the rule doesn't work when we consider the sentence as a whole, its meaning and any possible social function (ie in life.)
So, what's going on here is:
1. Using 'meaning' (semantics), grammarians describe what they see as 'structure'.
2. They define the structure using a term which includes some sense of this meaning - as with 'dependent' or 'subordinate'.
3. However, because this term is very general, when you test the meaning of the term in relation to the meaning of the sentence as a whole and its social function (ie in life), it falls apart.
Now things get even more unhelpful when it comes to those sentences which contain two clauses which are supposedly '...of the same grammatical type' which we can combine 'to form sentences using coordinating conjunctions.'
Here's the classic example:
So, according to the rule, neither of these two clauses is 'dependent' or 'subordinate', as derived from the meaning. They 'co-ordinate'. Again, ask yourself why would a person say or write one half of this sentence if they didn't want to say the other half. 'I'll take the train' does indeed 'stand alone' but so does 'you can take the car' but in terms of meaning and social function, the one depends on the other.
Now when it comes to the Grammar, Punctuation and Spelling test in England, everything that I'm saying here MUST BE IGNORED. You have to go along with the rules as described either in the Cambridge Grammar or in the 'glossary' provided by the government.
In fact, the distinction between subordinate and co-ordinate clauses is so hard to deduce from merely looking at one sentence plonked in front of you in an exam, teachers give children a mnemonic. That's how they get to 'know' or 'understand' the distinction ie absolutely nothing to do with the dubious grammar. The mnemonic is FANBOYS telling children that clauses beginning with, for, and, nor, but, or, yet and so are 'not subordinate'. When the question comes up - as it will do - tick the box to say which of four sentences contains the subordinate clause, just do your FANBOYS mnemonic, and it's the one that isn't a FANBOYS one that gets you (I mean the school) the mark.
Meanwhile, just consider one of these: 'so'. Make up any sentence you like with 'so' in it.
'I'm starving hungry, so I'm going to eat my beard.'
How - according to any system you like - 'so I'm going to eat my beard' is NOT dependent, NOT subordinate to 'I'm starving hungry' defeats me. You can claim, if you like, that it doesn't qualify or modify the preceding 'I'm starving hungry' but that's another matter.
So, remember, 'so' is a 'co-ordinating conjunction' and must ever more be so - whether that bit of terminology makes sense or not.
The best way (perhaps the only way) to remember this bit of 'knowledge' is by remembering the mnemonic.
Best of luck.