Let me start by offering two definitions;
Definition of Subjective
1. Proceeding from or taking place in a person's mind rather than the external world: a subjective decision.
2. Particular to a given person; personal: subjective experience.
Definition of Objective
1. Of or having to do with a material object.
2. Having actual existence or reality.
3. Uninfluenced by emotions or personal prejudices: an objective critic.
4. Based on observable phenomena; presented factually: an objective appraisal.
If morality is particular to a specific person then it is different for everyone because everyone is unique and experiences the world in their own unique way. Here is an example. The Earth is about to end and there is a man who believes, for whatever reason, that the only way to save humanity is by killing 32 people between the ages of 12 and 14. From his perspective he is doing the morally correct thing. From another persons perspective he is doing something immoral. So the action of murder, under a subjective morality, is both moral and immoral at the same time. This is directly contradictory, means NOTHING and is therefore useless.
Now, under an objective morality there is a clear distinction between moral and immoral. The above man still believes that he is doing the morally correct thing, but he is simply mistaken. The conclusion that the man arrives at, that murdering 32 people is acting in a moral way, stems from a false premise. Any conclusion that is drawn from a false premise is obviously false. Even if the conclusion is valid, there is absolutely no way that it can every be sound. It is simple logic. To know what is morally correct we need to arrive at the morally correct decision by basing our conclusion of true premises. We should follow the principles that the above definition of objective lays out. Following these things makes it more likely that we end up using true premises to arrive at the correct conclusion and therefore the correct moral choice.
To sum up:
1. All sound conclusions stem only from sound premises.
2. The conclusion that I am acting morally must stem from sound premises in order for that conclusion to be sound.
3. By following the definition of objective it is far more likely that one uses sound premises to arrive at a sound conclusion. That is far more likely then if we followed the definition of subjective. This is because the subjective experience of a human is tainted by biases and false beliefs.
In short, for a choice to be moral it must be the "correct" choice.