There are two types of claim: objective and subjective.
Objective claims have the same truth-value for everyone. For example, the claim that the Earth is cuboid is an objective claim; it’s either true for everyone or false for everyone. It isn’t possible for the Earth to be cuboid for me, spherical for you, but flat for everyone else, because whatever shape the Earth is it is only one shape.
Subjective claims can have different truth-values for different people. For example, the claim that running a marathon takes more than three hours is a subjective claim: for many people it is true, but for a good number of runners it is false.
The subjectivist fallacy is committed when someone resists the conclusion of an argument not by questioning whether the argument’s premises support its conclusion, but by treating the conclusion as subjective when it is in fact objective. Typically this is done by labelling the arguer’s conclusion as just an “opinion”, a “perspective”, a “point of view”, or similar.
This is one of those cases where the objectionable logic is so underdeveloped that it is difficult to pin down precisely what is wrong with it. Someone who just grunts “that’s just your opinion” is clearly trying to imply something, but their reasoning isn’t explicit.
They might have in mind something like the following:
(1) Your argument concludes that p is objectively true.
(2) P is subjective.
Therefore:
(3) Your argument fails.
This argument is fine as long as its premises are true, but where (2) is false it commits the subjectivist fallacy.
Alternatively, they might mean something like this:
(1) Your argument concludes that p is true.
(2) Many people don’t accept that p is true.
Therefore:
(3) Your argument fails.
This argument doesn’t commit the subjectivist fallacy; it has nothing to do with objectivity and subjectivity. Instead it is an example of an appeal to popularity, giving far too much weight to the opinion of those who don’t accept the conclusion of the argument, failing to recognise that even an argument for a conclusion that many people don’t accept can be sound.