Sometimes I encounter the phrase "there is no nonsense about him/her".
But what does this phrase tipically imply in general -- that the person is a serious one, that they deal with things in a serious manner?
[But in your (imperfect) paraphrase you seem to being misled by the 'false friend' 'serious'. This happens typically with speakers of French, though quite possibly Russian is similar in this respect: 'serious' can mean behaving with graveness/humourless/serious-minded... but it's more often used in the sense grave/weighty/considerable ... (in collocations such as 'a serious breach' or 'a serious matter')]
The interesting thing is that in Russian we have the same word - with several meanings that are very similar to the meanings of the English 'serious'. In Russian, we also can say "a serious breach" meaning that the breach is a considerable/significant, one that can cause big consequences.
But do I understand correctly that the pharse "there is no nonsense about him" can imply that the person is an important one -- he's a big deal so to speak, not to be sneezed at?
In my first post, by a serious person, I meant the person who, for example, always does what he promises (if you have a deal with him). In other words, if he says, "OK, I will do that", you can be sure that he will do, he will not give empty promises, i.e. "serious" as opposed to "light-headed".
I found one of the definitions of "serious" just in case my explanation hasn't been very clear:
Definition and pronunciation of serious | Oxford Advanced Learners Dictionary
4 thinking about things in a careful and sensible way; not silly. Be serious for a moment; this is important. I'm afraid I'm not a very serious person.