We usually use 到底 sometimes when you can't get the precise answers from the person you are asking.For example, if you ask your partner 他是谁?Then he said uhm.... he is new here,he is like 25years old belabela:p..Then you may need to say 他到底是谁?Personally think,it's a bit like Who is he exactly...So,emotionally,when people have a strong desire to know about something,a stranger's name, reasons or any other informations,and wanna get more precise feedback.
However,I would regard it as a little bit inpolite word,so I wouldn't use it often in formal occasions or even in my daily life.Because when use 到底 that means I have already run out of my patience listening to your stupid response,and I'm a little angry now and I need to know your exact answer immediately:)
Not professional enough,but hope these words can help you to understand.Thank you.