What is meant by the Objective Conception of Truth? (Protagoras)

The objectivity of truth has been the focus of many philosophers, including Nietzche, Plato, and Kierkegaard. To better understand the "objective conception of truth," let's break down the phrase into its individual components. First, truth, or that which is factual. Conception of truth is referring to how we understand and think about truth. Finally, the term objective refers to that which is not dependent upon personal thoughts or experiences- things which are regardless of how we perceive them, or if we perceive them at all. With that, the objective conception of truth implies that is a factual truth which we can come to understand, but which exists regardless of our own perceptions. The opposite would be subjective truth, which may be different for many people because it is based on personal perceptions. 
The idea of objectivity has plagued numerous scholars because being human is a highly relative experience. For humans, no knowledge exists in a vacuum, safe from the taint of emotions or prior experience. Nonetheless, many philosophers and scientists seek to understand that which is objective in the world through rigorous thought and experimentation. For truth to be objective, it must be free of opinion or bias, and must be fixed in the sense that even if someone were not around to observe the truth, it would still be true. 
Protagoras was a fifth century philosopher from Greece who was quite in opposition to any concept of objective truth, though he was not necessarily subjective. Protagoras was one of the first thinkers to elaborate the idea of relativity, or that all "truth" exists in relation to the perceptions of an individual. For him, reality was understood based upon one's experiences in the world.
At the risk of simplifying too much, let's compare objectivity, subjectivity, and relativism in the following example. Imagine someone has been gifted a dozen roses for a special occasion. We could count the roses and objectively say that there are twelve. Regardless of whether or not someone is in the room to look at them, there are a dozen roses. Now, the person receiving the flowers thinks that roses are beautiful- this is a subjective feeling. We could ask, "Are they the most beautiful roses you've ever seen?" That person would have to consider whether these dozen roses, relative to others, are the most beautiful.
Protagoras was both relativist and agnostic, so it may be safe to say that he held suspicions on the objectivity of truth (there may well be an objective truth) but the human conception of this truth was entirely relative.