Discrimination (which is, as has been said, different from prejudice) is illegal, but can be difficult to prove as screening out other reasons for choosing one candidate over another is all but impossible.
However, prejudice can (not always though) explain why particular assumptions are made about one candidate over the other. Many people think that people like them are going to fit in better with other people like them, and if most of the team are middle aged middle class white men, a young black woman has a harder job to convince an interviewer that she could fit in too.
However, white privilege is not just about discrimination. It's often about what doesn't happen, such as not being stopped and searched, or followed round a supermarket by a store detective, stopped in airport security more often, or asked where you are from all the time. It can be small things like being able to find the right shampoo for your hair without travelling to a particular part of town, or being able to find your child toys that represent her and her family. They are the things that many people do subconsciously, because our lives have always been like that, and it's more difficult to spot things that we don't experience. People can do things like looking nervous when someone with a backpack and brown skin gets on the train, assuming that you or a loved one didn't get a job because of a quota, or that a person of colour must have got theirs for the same reason, believing that there is such a thing as 'playing the race card' and so on without even realising they do it and that it is hurtful to those on the receiving end.
I second Wyllow's suggestion of reading the 'White Supremacy' book. The title is maybe not the best, but it is explained early on why that was chosen other than 'white privilege'. White privilege is also, IMO, an unfortunate choice of words for the concept, as a lot of people assume that it means a refusal to believe that white people can be poor, exploited or passed over (now or historically). It doesn't mean that at all. We can be all of those things, and many are, or our ancestors have been. What we don't have is constantly to have to prove ourselves in all sorts of ways (eg that we are not muggers, terrorists etc) and not having small but relentless snubs and micro-aggressions to deal with on a regular basis.