The difference between objective and subjective is the difference between facts and opinions.
If something is objective, then it is true no matter what anyone thinks or believes about it. If something is subjective then it's just based on a person's own preferences and doesn't hold any truth value.
'The Earth orbits the Sun' is an objective fact. 'AC/DC are a better band than KISS' is a subjective opinion. (I'm not endorsing that view - I can't make that commitment)
So what about 'objective moral values'? Are the things we believe about morality true facts or just our own opinions? Is it really wrong to hurt people or is it just something most of us don't like to do?
It's important to realise the difference between 'objective moral values', 'absolute moral values', and 'universal moral values', which can sometimes be confused. Objective moral values would be facts that can't be denied. Absolute moral values are simple rules that are always true in any circumstance e.g. it's always good to love other people. On the other hand 'you should not kill', is on the face of it something that sounds like a good value, but in some circumstances, killing might be the right thing to do e.g. for food, mercy/euthanasia, self defence/just wars. So 'not killing' is not an absolute value.
Universal moral values are ones that everyone subjectively agrees with. So (WARNING: tired old example incoming) if the Nazis won WWII and brainwashed everybody in the world so that they thought murdering Jews was a good thing, it would be a universal moral value, but it wouldn't necessarily be an objective moral value.
I'd hope that we all agree that murdering Jews is bad/wrong/evil. I'd like to state for the record that I do believe that murder (of anyone) is evil.
But is it just my (our) opinion? That's the tricky thing about morality.
No one is going to put you in prison for a subjective belief that Lynrd Skynrd is a better band than The Eagles (not committing to that view). Most people find it pretty annoying when someone tries to insist that their personal preference is factually better than someone else's personal preference.
We see opinions as having equal weight between people. No person's opinion matters more than anyone else's. It doesn't even matter if a majority prefer one thing over a minority, opinions don't have truth value. It doesn't matter if 70% of people prefer chocolate to strawberry ice cream. It doesn't matter if 99% prefer it. It doesn't become a fact just because of a majority vote. Just like with the Nazi example, a 100% preference vote is a universal value, not an objective value. (Let's ignore the question of whether some bands/flavours are objectively better than others for now.)
But when it comes to morality, we have government, laws, law enforcers, courts, juries, and all sorts to make sure that everyone lines up. Are we just enforcing the popular vote? Are we just insisting that everyone eat chocolate even if they don't like it? Or are we trying to live by what's real?
If you say it is wrong to murder, are you saying that you don't like it or that it is really wrong? The moment you say that murder is really, truly wrong, you're saying it is an objective truth.
But can moral values be objective? The only way that they can be is if they are grounded in some kind of object that you can point to and say "That's what good looks like" or "That's what evil looks like". From there, you can compare stuff to that object and figure out whether it's similar or not.
Let's take colours. Green is objectively green. Lime green is a bit different, but it's almost identical. Blue is sort of an ingredient of green, but it has something missing. Red is the opposite of green. There's no green in it and it is not in green.
So if moral values are objective, then when we say 'murder is wrong', it's like saying that 'red is not green'.
But if moral values are subjective, then when we say 'murder is wrong', it's like saying that 'I don't like red'.
