I am not really sure when to use "a time when" or "the time when". Would someone make it clear for me?
1-At the time when I was shepherd, one could only see wolves with binoculars.
2-This is the time when I'm finally able to relax.
3-There used to be a time when I loved my mom. (Isn't she or he talking about a specific time?)
4-Anna Akhmatova lived at a time when poetry mattered.
This is precisely the usual distinction between definite and indefinite articles that one usually experiences - is it referring to a time that is unique and specific (though it can be a long period of time), or is it referring to a time that is merely one example. It is not about whether it is a specific time, but whether that time is unique in some way. There are also some specific differences in different sorts of use, some of which conveniently show up in, or in relation to, your examples.
In your first example, when I was a shepherd can be taken to mean a period in that person's life when they were a shepherd. Even if that time had breaks in it, it is unique and well-defined for them, and refers to the whole time - whether it is contiguous (all in one piece) or not. If they were to use a time when... it would mean some more particular point in the time when they were a shepherd.
In your second, it suggests that the time they are referring to - and time might actually mean situation in this case - is the only time when they can relax. If they had used a time when, it would mean there were other times that they could relax, but 'this' was one of them.
In your third example, there was a time or there used to be a time is a turn of phrase, a way of saying that something was true at some time in the past. There was the time is used in different situations. For example, someone might say "I don't know that I've ever been on a ferry" and someone might reply "of course you have, there was the time we went to Calais". Essentially, there was a time is used for statements of general truth about some time in the past, while there was the time is used to discuss actual events. Exceptions probably exist, but that's a good rule of thumb.
The fourth case is very clear and easy to understand why - it suggests that there have been multiple times during which "poetry mattered", and Anna lived during one such time.
I think the best explanation is that the same general rules regarding the definite article ("THE") and the indefinite article ("A") are at play, but it's harder to conceptualize with such an abstract noun as "time".
The best way to show what I mean is by example.
1-At the time when I was shepherd, one could only see wolves with binoculars. The time when this guy was a shepard is a specific, discrete block of time. During that time, there was only one way to see wolves. (DEFINITE ARTICLE)
2-This is the time when I'm finally able to relax. This one's trickier. Let's imagine what scenario when this sentence would sound right. You're sitting by the pool with a nice drink, as you do every day at 3 PM. This sentence is a somewhat exagerrated statement that this is THE specific time when you can actually feel relaxed. It may not be literally true, but think of how a weird a similar sentence would sound with the indefinite article: You're at a great bar, and you want to tell your buddy next to you how cool you think it is. "This is THE place to be!" is more idiomatic than "this is A place to be", which while technically correct, is weak and meaningless.
3*-There used to be a time when I loved my mom. (Isn't she or he talking about a specific time?)* It's not specific enough to use the definite article. If the sentence were "Last month was the time when I love dmy mom", then you'd be right. But the speaker is just saying that a time when that was true used to exist. (INDEFINITE)
4-Anna Akhmatova lived at a time when poetry mattered. There may be many different times in history when poetry mattered. We don't know which one Anna lived during, but she lived in one of them. (INDEFINITE)
N.B. - There is also an idiomatic usage worth noting. For example, if a judge asked you whether you were employed when you robbed the liquor store last month, the idiomatic English response would be "At the time, no".
