Objective, Subjective, Intrinsic
There are three major views of the nature of values. The first two, subjective and intrinsic, are often seen as a dichotomy. Objectivism accepts an objective view of values.
Let's start with subjective values. Basically what this means is that something is a value because you choose it to be. Anything you decide is a value is valuable. There are no objective standards when it comes to morality. You do whatever you want, and pursue whatever value you happen to want. Everyone chooses their own values, and there is no possibility of objectively judging the values of other people.
The alternative to subjective is objective. Since subjective values come from the subject, then it is sometimes thought that objective values must come from the object. This is what Objectivists call intrinsic values, though. It means that the value is supposed to reside inside the object itself. Water is of value, right? If we dismiss subjective values, then one possibility is that the value isn't just our own opinion, but it actually is an aspect of the object. So water must have some 'value' characteristic that we can somehow observe. This is considered objective because the 'value' is out there, where anyone can see it. Except of course nobody explains how exactly we observe this 'value' characteristic.
As I said, that was intrinsic values. The object is intrinsically valuable, and we just have to observe the fact. The intrinsic theory escapes the subjectivism, but it has the side-effect of being entirely wrong. Also, while it explains why people may act to gain and/or keep an object (it doesn't really explain it...just states it), it doesn't quite explain other values, like happiness, self-esteem, sense of achievement, etc. If physical objects are valuable because some magical value stuff emanates from them, what about non-physical values?
The alternative to these is what Objectivists call The Objective Theory of Value. Instead of postulating that a value resides in objects, or is just a figment of our imagination, it holds that there is a relationship between the value and the valuer. This theory can also be called the relational theory of value. It says that something is of value to a specific person, for a specific reason. You value water because you need it to survive. You value chocolate because it tastes good. You value Objectivism because it provides you with a framework for understanding your own life better.
Notice also that because the values are relational, they're also contextual. I may like a glass of milk because it tastes good and has calcium, but someone else may be lactose-intolerant. Different people will evaluate things differently due to the fact that their needs are different. Similarly, you may value a glass of water a lot when you're thirsty, but not much at all if you're not. The relationship between the value and the valuer change over time, depending on context. This is something that an intrinsic theory cannot account for. If the value did exist independent of anyone to value it, then it should be the same every time, and to every person.
Since the values are relational, you can't talk about something being valuable in an abstract, disembodied way. It is always a value to someone, for a specific reason. The whole discussion of values presupposes these conditions. You need an entity that's capable of acting towards a goal, and you need to have some point or reason for the action. Only then does the concept of value make any sense. Additionally, the entity must be faced with an alternative, or again the concept of value is meaningless. If there is no choice in the action, then there is no point to the evaluation.
Before finishing, it should also be noted that intrinsic values, in practice, act as subjective values. Because there is no explicit means of determining what is or isn't a value, you basically just have to guess. Or follow what other people say. Or what the bible says. Or whatever you feel like today. The intrinsic theory or value just allows one to rationalize their values, and try to claim the mantle of objectivity.
I discussed intrinsic values in more detail in my article Inner Peace on this site. Since an intrinsic value is not relational, it claims to have value in and of itself. How do you compare two intrinsic values if you have to make a choice between them? What standard would you use to compare them? The intrinsic theory holds that the values do exist as part of the object, but it doesn't say how you gain knowledge of it, and so it doesn't give you a means of comparing them. And so you're left with the same as subjective value theory. You think it has such and such amount of value, and that's good enough. You make trade offs by whatever you end up feeling like.
How do these non-relational values compare with relational values? If you think animals have some intrinsic value in staying alive, how do you compare that to values such as having a steak for nourishment, having a fur coat for warmth, having a leather jacket for protection from the elements, etc? Although both claim to be values, they don't actually have a common measurement, because they don't have a common method of identification. Relational values are valuable to a person, for a reason. Intrinsic values are not. You can't compare them based on a single cognitive standard. You're left with comparing them based on how much you desire them. Since any kind of value can lead to an emotional desire, that is the only standard left of comparing them. And if that's not obvious already, it means that by accepting intrinsic values, you need to treat everything as subjective values in order to compare them. If you just had relational values, you could compare the different ends which you're accomplishing. You could compare the purposes behind the values. But once you accept a value that has no purpose, you can't follow that method. You need to choose the only thing they have in common, and that's your level of desire. Mixing a little poison with your food leaves the whole thing poisonous.