Normally when we think of prejudice we simply think of certain negative preconceptions we may have about the object under consideration. Hume, in "Of the Standard of Taste" insists that lack of prejudice is one of the characteristics of the good judge. But what is this lack of prejudice? It turns out to be something very positive and very specific. We first learn that every work of art should be surveyed from the point of view that is required for the performance. Lack of prejudice is taking this point of view.
Hume explains this rather oddly. He speaks of how an orator must take into account the point of view of his audience, and especially needs to address any prejudices they might have against him: he needs to acquire their good graces before he can convince them of anything. So, are we to act like such an orator when we appreciate art without prejudice? No. Hume is simply bringing up the orator as preliminary to the main point. Now, he turns to the "critic of a different age or nation" who, upon looking at the speech of the orator in question, needs to take all of this into account. He must "place himself in the same situation as the audience in order to form a true judgment of the oration." One might think that he should put himself in the place of the orator himself. But, for Hume, lack of prejudice is a matter of trying to put oneself back into the time of first production or publication and trying to make oneself susceptible to the powers of the orator or author, as an audience member of the time might have been.
It is only after this that Hume brings up the point that would normally come first to mind when thinking about prejudice, that if we are either a friend or enemy of an author (presumably a contemporary one) we should put these feelings aside and consider ourselves to be men in general. "Don't be prejudiced" here means "don't think about your friendship with or enmity against the author" and don't let it influence you, even unconsciously.
What is odd here is that in the example regarding the past we are supposed to immerse ourselves in the particular situation of the audience, whereas in this example we are to detach ourselves from our own particular situation.
Hume tries, however, to combine the two when he says "A person influenced by prejudice, complies not with this condition; but obstinately maintains his natural position, without placing himself in that point of view, which the performance supposes." The general idea, then, is lack of prejudice is placing oneself in the point of view supposed by the author (perhaps even with the prejudices the author's audience originally had and which the author is trying to overcome!)
Although trying to put yourself into the position of the intended audience is a good idea I also think it valuable sometimes to switch to another position that is closer to one's own "natural position." We can more strongly feel what is said when the work speaks to us as we are and not just as we would be if we lived in another country or time. I think we need to toggle between the two positions (to use Peg Brand's term).
Another oddity is that when Hume, at the end of his essay, begins to speak of innocent sources of variation he stresses our inability to enter into other times. For example, an older man cannot enter into the sentiments of a younger man and hence, presumably, can no longer appreciate the erotic poetry of Ovid. But isn't that what "lack of prejudice" was all about, i.e. overcoming one's natural position? He says that we, here, cannot "divest ourselves of those propensities which are natural to us." But that is what he was requiring of us previously when he said that we should lack prejudice! Of course we are going to be "more pleased, in the course of our reading, with pictures and characters, that resemble objects which are found in our own age or country, than with those which describe a different set of customs": but lack of prejudice is supposed to overcome this. Also, isn't it hilarious that the example Hume uses for something extremely difficult to overcome is seeing a princess carrying water or a king cutting his own meat -- something that doesn't bother us egalitarians at all?