I can't really find a definition that explains the concept of "White Privilege" in a simple way, but what I have understood so far is that it means white people will benefit or enjoy more power and opportunities than visible minorities.
As you mention, it refers to a racial concept of privileges enjoyed by white people:
White privilege (or white skin privilege):
is a term for societal privileges that benefit white people in Western countries beyond what is commonly experienced by non-white people under the same social, political, or economic circumstances.
According to McIntosh and Lee, whites in a society considered culturally a part of the Western world enjoy advantages that non-whites do not experience.
Academic perspectives such as critical race theory and whiteness studies use the concept of "white privilege" to analyze how racism and racialized societies affect the lives of white people.
From an historical perspective:
Some scholars attribute white privilege, which they describe as informal racism, to the formal racism (i.e. slavery followed by Jim Crow) that existed for much of American history.
In her book Privilege Revealed: How Invisible Preference Undermines America, Stephanie M. Wildman writes that many Americans who advocate a merit-based, race-free worldview do not acknowledge the systems of privilege which have benefited them.
A commonly cited example by writers such as Ta-Nihisi Coats is the fact that, statistically, whites and blacks use drugs at roughly the same levels, and yet blacks are overwhelming targeted by law enforcement. In a country that practiced slavery upon its founding, and that replaced that institution with Jim Crow laws, and in which whites males still hold virtually all political power, it is politically much easier to target black communities than white. The idea that mass incarceration has now replaced the outlawed Jim Crow restrictions has gained currency because of this unequal treatment afforded the races. White people, in short, are not harassed when they use drugs--it is in fact assumed that whites do not use drugs (though now deaths from overdose among white Americans are increasing dramatically), while blacks are harassed whether or not they actually deal or use drugs. That's white privilege.