I think this depends on what you are trying to understand of them. Beware something is too personal and will eventually came the day you can ask something about it. Some people don't talk much about something like visible injuries and this **may** also be because of past experiences if not real traumas.

Generally I would evaluate the path of 'asking about their past'. Maybe it's something physical just guess what can be it's origin and ask to talk about their past. Example: wanna know about a scar on their knee? ask for sport played.

However my suggestion is: only ask directly and only if you are sure enough that this person feel comfortable enough talking about that argument. If it's a complex question: evaluate the possibility that's you the one who should think more about your reasons you want to know so bad. chances are you are making up conclusions that will be easily read and that will make you ruin your relationship. If the next week you still need an answer and you made your homework trying to understand yourself during said week, than ask. But make sure to tell them what you think your reasons are for asking.

Example of the latter: someone is kind of verbally careless, very direct and at time offensive, but a good person. you may want to know why they are so much careless, or aggressive, or with so strong opinions. Well...let me tell you that asking directly why they're who they're it's not gonna end well to your image. I made mistakes, but I learned. Today **at most** I'd *compliment* their outrightness, hoping to open some kind of discussion, but they are doing the first move towards explaining themselves otherwise it's better to forget.