The significance of this letter is that it tells us something about the attitudes of freed slaves towards their masters. This is very important, especially given the attitudes of many modern historians.
Today, historians feel that it is important to look at the lives and thoughts of the "little people." They think that historians of the past focused too much on the doings of important people like government leaders and not enough on the lives of common people who were not famous or important.
This is why the Jourdon Anderson letter is so significant. Slaves were pretty much the epitome of people who were not famous or "important." At the same time, they were part of one of the most important chapters of history. Therefore, it is important to historians to know how they felt.
Sadly, there is not much material about how slaves felt. There are a few slave narratives in book form. There are oral histories collected in the 1930s. Both of these are valuable sources, but both are limited. Slave narratives were typically written before the end of slavery by slaves who had escaped. They were written for an abolitionist audience. Both of these things make them a bit skewed as sources. The oral histories, obviously, were collected long after the fact from people who were quite young at the end of slavery.
By contrast to these things, Anderson's letter is a contemporary account of a freed slaves attitudes towards his master. This makes it a relatively rare window into the lives and attitudes of freed slaves. For this reason, it is a significant source for historians.