Institutional racism is when racism is built into the way a particular social or cultural institution operates. In effect, a social institution (a school, a corporation, a political system, a church) operates in a way that assumes people of color are less important and valuable than white people, that people of color don't "count" as fully or needn't be paid attention to in the same way. Sometimes this institutional racism is overt and official, such as when (until the 1960's) Black people in many southern states were excluded from state colleges and universities even when Blacks paid their share of state taxes to support those colleges. Sometimes the institutional racism is covert and unofficial, such as when a school adopts a history textbook that "neglects" to include the lives and accomplishments of people of color, implying that those people who do count, who make history, are all white. Either way, a social institution acts in a way that tends to put people of color at a disadvantage, a way that discriminates against them and deprives them of equal benefits or respectful treatment.
Such institutional racism is often more damaging than personal prejudice. It always hurts, of course, when even a single person treats you badly and unfairly because of your skin color or your racial identity. But social institutions have much more power than individuals, and can do more damage when racist assumptions are built into how they operate. It hurts when someone uses a racial slur against you, but is perhaps more damaging in the long run never to see your image in mainstream television programming, or in your school's history books, or to be denied a mortgage loan because of your color.
Another reason institutional racism is damaging is that it lets individual white people imagine there is less prejudice and racial discrimination around than there really is. Institutional racism is often kind of indirect, kind of vague--no one seems to be doing it, no one seems responsible. In a way, institutional racism is a way of saying that society discriminates on behalf of white people, so that white people do not have to do it for themselves. White people underestimate the power and pervasiveness of racism because they no longer have to discriminate against people of color personally; they feel less guilt about, or responsibility for, the lives of people of color around them.
Yet white people may still benefit from the discrimination practiced by the institutions around them--if corporations put toxic waste dumps in the neighborhoods of people of color rather than in white neighborhoods, for example, white people benefit from the racist decisions made by corporate leaders even if those white people aren't aware that such decisions have been made. Sometimes this is called "white skin privilege" or simply white privilege.
White privilege is a term that indicates the kinds of benefits and privileges a white person accumulates in a society set up to reward white skinned-people. Individual whites may not want, or even know that they receive, such privileges; nevertheless, such privileges are real. For example, white people who go into a nice department store are usually treated as if they belong there, as if they might be a valued customer, and are treated with courtesy; on the other hand, many Black people report being followed around by clerks in those same stores, treated as if they are shop-lifters rather than customers, treated in a demeaning and mistrusting way that is very painful. Most white people, if shown this situation, would agree it's unfair; the point here, however, is that when you have a society in which white people are at the "center," are regarded as the most fully legitimate and human people, are the kind of people who “get the benefit of the doubt,” then white people do get treated better and more fairly even when they don't believe in such treatment and even when they neither seek nor are aware of it.