All verbs have -ing. Some verbs have its noun form that often ends with -ment, -ion, -ism and so on.
I want to know the difference.
Your explanation was very good.
Your explaining was very good.
The -ing form, as you say, can be made from more or less any verb. It refers to the act or activity of the verb.
So Your explaining was very good says that the act of your explaining was very good: perhaps you spoke well, perhaps the hearer was very much in need of an explanation. It does not directly say anything about the content of your explaining.
Explanation is an abstract noun derived from the same root as explain. (As you indicate, it is not predictable from either grammar or history whether this word exists or not: it just happens to, whereas explainment doesn't). It means the content of your explaining. Your explanation was very good says nothing about how well you spoke, or how much the hearer needed it explained: it says that the explanation you gave was clear and comprehensive, or perhaps had other virtues, such as being funny.