Ethnocentrism is the feeling that your own ethnic group is superior to all others. It is generally seen as a negative thing today because it can lead to very bad things. It can lead to systems like segregation and apartheid. In the most extreme cases, it can lead to things like the Holocaust. In its most benign forms, it leads to a lack of understanding and toleration. It leads us to think that those who are not like us are not as good as we are.
Cultural relativism is the idea that we should judge each culture from its own point of view. In other words, we should not apply one group’s values to another group. The major benefit to this is that it helps to avoid the negatives associated with ethnocentrism. It promotes understanding of other groups. The problem is that it can lead, in a sense, to a complete lack of direction. If we think that all cultures are morally equivalent, it is hard for us to be assertive about preserving what is good in our own culture and trying to keep out the bad aspects of other cultures. Ethnocentrism could be good in that it allows us to do this.
To be ethnocentric means to evaluate another group or culture solely by the standards of your own. The way your group acts is the only right way to behave, and your customs and beliefs are superior to those of other groups. The positive of this is that it offers confidence and assurance to the culture. It helps the group remain cohesive and centered. The negative is that ethnocentrism can lead to arrogance and a tendency to ignore the useful and even superior knowledge or mindset another group might offer. For example, in Jared Diamond's book Collapse, he argues that the Scandinavians in Greenland could have survived if they had adopted aspects of Indian culture, such as building waterproof fishing kayaks, because the native culture was better adapted to the realities of the climate and ecosystem. But ethnocentrism led them to reject native ways as inferior and insist on trying to run farms, and so they perished.
Cultural relativism, on the other hand, means evaluating a culture from the point of view of that culture. If ethnocentrism means viewing another culture from the outside, culture relativism is the view from within. It is positive in that it does not impose the values of one group on another group and does not judge another group as inferior simply because it is different. Its negatives include what some have called "neo-racialism," which means it is possible to overlook the poverty or abuse, for example, of another group by saying it is simply part of their culture for them to be impoverished or to practice mutilation on people in the culture without their consent. If there are no universal values, moral relativism can follow, allowing anything to be accepted, and that can create a problem, if for example, we want to condemn practices like genocide.