Right, so it's a bit like this:
The most popular theory of truth is the correspondence theory. Essentially, for a statement to be true, it has to correspond to a state of affairs; it has to, in some way, represent the way things are.
For example, if I say that it's true that it's raining here now, for that statement to be true it has to be raining here, now.
Seems pretty obvious, no? Well, this theory isn't bulletproof. Firstly, there are verification issues; How can we ever be sure something is true? But this isn't a problem with the theory per se.
A better objection is to do with the way we divide up the world into classes and properties, some of which may be arbitarty or based on cultural values. One tribe (although I hear "tribe" is no longer a PC term, perhaps "mobile people" or something is better) classes twin babies as birds. Their definition of birds includes twins. Are they wrong?
Perhaps the strongest claim is that the correspondence theory is simply uninformative.
Whether you buy into these problems or not, some philosophers do and went in search of other theories of truth. One of these is absolute relativism.
You'll often hear people arguing about values or experiences like this:
Person 1: "That's not true."
Person 2: "Well, it's true for me!"
This implies that there's a sort of truth different from the correspondence sort, which has something to do with the person making the statement.
Absolute relativists say that all it is for me to say something is true is to say it is true for me, or that I believe it to be true.
In other words, if I think that it's Thursday then that's true, really true. If you think it's Tuesday then it's true, too.
a lot of people are attracted to this idea. It sorts out those nasty epistemological proplems. Gorgias the sophist did, and it pops up the whole time in postmodern thinking.
It has some interesting consequences too. If I say something is true and you say it's false, we aren't in any way disagreeing. It's like me saying I've got a headache and you saying you don't. However, while you can claim I don't have a headache, it gets much more complicated when people start assessing the validity of others' truth claims from a relativist standpoint.
e.g. "so are you saying that X is false for me, or false as in true for you, or that it's true for you that X is true for me?" etc
So does relativism work, then? well, it depends exactly how one formulates it, but probably not. Any theory that seems to do away with the real state of affairs is dubious. It's true for me that there are no cars coming, so I don't look before crossing the road. Funnily enough, I'm not immune to accidents.
Another objection is that's simply not what we mean by truth. When we say something is true, we are trying to make statements about the way the world is, and we believe others can be wrong.
Finally, the relativist theory of truth contains the seeds of its own destruction. For me, the correspondance theory is right and the relativist theory is wrong. The relativist theory would accept that in this case, it is itself false. That seems ludicrous.
In serious philosophical thinking, absolute relativism is pretty much discredited. A number of more subtle theories of truth are out and about in current thinking, though.
An as for moral relativism, well that's quite a diffferent problem...