But what is morality?
Morality is a means by which we humans organize our survival of this world and each other. By extension, it is also a means by which we increase our common welfare. We do all this by endorsing character traits, rules, and actions that are conducive to these ends, and reprimand them when they're destructive of these ends.
Is it absolute, based on irrefutable standards?
I think morality itself is pretty close to absolute. The specific standards for evaluating character traits, rules, and actions may be refutable by empirical testing.
Is it based on premises derived from standards?
No, it arises from real-world experience with actions, their consequences, and the harm or benefit these consequences cause for people. The standards come afterwards, as a codification of these experiences and extrapolation beyond them.
Is it relative, varying according to one's world view?
Only to the extent that identical actions have different impacts on human well-being in different parts of the world, and in different periods of history.
Does it require judgements based on our simple understanding of good and bad?
Our simple understanding of good and bad is a good start, but morality also requires the abstraction of this understanding into rules that are internally consistent and useful for informing our behavior in situations we haven't been in yet. One possible byproduct of developing these rules is the insight that our simple understanding was incorrect.
I am guessing we would all prefer to live in a "moral" world. What would that mean?
Actually, I don't think this is true. If I could live in a world that is immorally rigged in my favor, I might well prefer that. But if I have to live in a world where the rules are the same for everyone --- and I do --- I want those rules to take away as little as possible away from me in freedom while giving me as much as possible in security and welfare. For example, "murder is wrong" is a good moral rule because I lose very little by being barred from murder, and I gain very much by others being barred from murdering me. I think rules are "moral" to the extent that they offer us good tradeoffs in this sense.