In a nutshell, cultural relativism is understanding a culture other than your own objectively, without laying the rules of your own culture into your understanding. I would argue that empathy—the ability to experience life from somebody else's framework—is an essential component of being able to practice cultural relativism in one's research.
Its importance in studying another culture lies in the depth of understanding that you are able to obtain about that culture. If you do not approach a new culture with an open mind, you will be far less likely to be able to understand the details and the traditions which make up that culture.
Let's look at arranged marriage, for example. As a Westerner studying this issue, you may feel completely confused by this, because in American culture, we choose our own spouses, and any other approach may seem unfathomable. If we remove the Western mindset from our understanding, however, it becomes easier to understand the purposes that arranged marriages can have within a societal structure, such as allowing the consolidation of family property.
Cultural relativism is of particular importance when studies are being done about cultures which have been oppressed or marginalized. For example, if one was doing a study about Aboriginal Australians, one would have to acknowledge the disrespect with which this culture has been treated in the past and use the principles of cultural relativism to approach the study with the necessary care and sensitivity.