Big brother Google says, one of the multiple meanings of “白” is "gratuitous" = 免费的. Baidu also gives “白” as "free of charge, gratis". That seems to be clear enough.

It has a little different meanings in different sentences. free of charge; without payment; / for nothing; given or obtained without the need for work or effort. 1、他什么忙都帮不上，即使他白给我帮忙我都不需要他的帮助。 There is nothing he can do to help. Even he comes to help me for nothing, I will not need his help. 2、因为计划调整，我们过去一周的工作都是白费力气。 Because the plan was adjusted, all our work last week was for nothing/in vain. 3、你爸爸告诉你，别人的东西不要随便收，即使白给你的也不要随便拿。 Your father told you that do not take other people's thing, even it's given for free/ without payment.

It means something that you don't like it ,you refuse accept it. Especially, in emotion ,you don't want to have it.

- Let's have lunch in that restaurant. - OMG! Their food tastes like feet! I will never go there even it's free! or I will never go there even they give me money! I will never go there even it's free ---- 就算白吃我都不去 I will never go there even they give me money ---- 就算倒贴钱请我去吃我都不去 "倒贴钱"：Logically, if you go to a restaurant for lunch, you should give money to the restaurant, but here, you want to say: even the restaurant gives you money to invite you to have lunch there. Things like "restaurant gives money to client" is called 倒贴钱. （就算）.....我都不 + verb means I will never ever do that. （就算）白给我都不要：it means that you are very hate that stuff, you will never take it even it's free. this is a kind of expression to describe that you dislike a lot some thing. In english we have some expression like "this is the last man that I want to see" meaning you don't want to see him. But you don't just say "I don't want to see him", you change another way to emphasize some emotion. "白给我都不要" is just like this. You don't just say 我不想要, you say: 白给我都不要 to emphasize your emotion.