Interesting to hear people's responses to this question.
I tend to think, as others who have replied appear to imply, that an objective interpretation of the question does come against the problem that there doesn't seem to be anything in a depersonalised view of the world that we would call by the name 'matters'. I would be interested in ideas that might suggest that there is objective 'mattering'. Of course, I take it that some religous views of the world would hold that value or 'mattering' is inscribed in the world independently of whether you or I believe this is so. I certainly thought so for many years but in the end was not able to prove it to myself either philosophically or experientially.
I also tend to think that a subjective reading of the question is problematic. While we are all, it appears, more or less orientated to behaving as if some things do matter to us as self-interested individuals e.g. to be full rather than hungry, feeling pleasure rather than pain, and so on, it does not follow that we would categorise these things as 'mattering'. It seems to me that the idea of 'mattering' is one that would transcend sef-interested concerns. I mean, okay, you can be happy, I can be happy, so many people can be healthy, animals can be in pain or not, we can pollute the planet or not, but there is a sense that despite these things appearing to matter to the individuals involved at the time, in the larger scheme of things or at the end of the day, all of this will pass, is cosmically relatively insignificant, and will mean nothing or matter not beyond that very localised sphere of concern.
In my life, I want a sense of mattering that can extend beyond this. Indeed, it matters to me whether there is such a thing.
I tend to think that, philosophically, the problem here is a misunderstanding of language. That is, the term 'matters' in its transcendent sense, only corresponds to an idea rather than to anything that is the case in the world. Some of us, at least, seem to have been conditioned to believe that 'mattering' actually exists in the world, is a real thing, when in fact there is no mattering in the world, only in our heads.
But mattering is real, for me, even if it something that I recognise only through the absence left by all the things that don't matter. But then, this suggests that mattering is just the necessary conceptual counterpart of not mattering, one half of a mutually self-sustaining pair, a way of thinking in language about the world but not actually corresponding to anything actual about that world.
So, philosophically, I can see how the problem dissolves. Can this carry over into my life existentially, though?