I couldn’t find this in the dictionary, here is the context:" Besides, the problem with history is that there’s just so much of it. There’s no way I could keep it all straight."
There are some meanings I could try to guess here: “memorize”, “keep it up to date”, “keep it organized”…
What’s the real meaning?

In this context I think it means “keep it organized”. Your other guesses could be right in other contexts.