The sociological imagination is the ability to look at things in the context of our own lives and societies (or those of other people). In other words, it is the ability to think about why certain facts about societies come to be, rather than assuming that they are natural. Let us apply this to a belief that people have for which there is no evidence.
If we use the sociological imagination, we can put ourselves inside the society that holds this seemingly illogical belief. We can then examine the society to try to figure out why that belief makes sense in the context of that society. So, let us say that there is a society that believes that women are mentally inferior to men. We can look at that society’s history and context to see why it would hold that belief. Perhaps, for example, the society depended on manual labor until very recently. When manual labor is important, men have an advantage because they are, on average, stronger. As men came to dominate the society because of this, they built up an ideology that justified their power. They concluded that they were superior and they taught their entire society to believe it.
Thus, the sociological imagination helps us to try to understand where an unfounded belief comes from.