May somebody explain this expression about "though" for me?

It appears to be an adverb in this case and synonymous with however. It plays the same function as the word but would at the beginning of the clause.

It would've been useful to know the preceding sentence, but since we don't, I'll make one up.

Consider the following:

He went on holiday, but he wasn't there long because...

Now, say, we want to separate the two clauses into individual sentences. It's rather difficult to say why it may have been done this way with this sentence being presented in isolation.

He went on holiday. But he wasn't there long because...

This is somewhat unconventional. It's not necessarily uncommon, but some don't like it. One solution is to use another word carrying the same meaning, i.e. expressing a contrast:

He went on holiday. He wasn't there long, though, ...

There are many other ways of doing it (e.g. with although at the beginning of the clause). There could also be many reasons why it was written this way, for example, a more formal register.

I can't go into any more detail, though, because too little context was provided.

I have added a little context:

He wasn't there long, though, because his mother passed away just four years later [and he inherited her house.]

Though is a free modifier: it can be placed at the beginning “Though he wasn't there long because…” or omitted.

Free modifiers modify the entire clause/sentence adverbially.

Compare other possible free modifiers:

He wasn't there long, fortunately/in reality/questionably, etc, because his mother passed away.

Fortunately/In reality/Questionably, etc, he wasn't there long because his mother passed away.