Why is it that some (yet not all) people may struggle to retain information unrelated to what they are interested in? It seems to me that some people find it difficult to retain information that is not naturally salient to them. This isn't the case for all people, however. There exist people that will put in the effort to retain and use information related to material that is inherently uninteresting to them, particularly in a school setting. Is it the case that the latter group has more of a conscious control over what is salient to them at the time? Is this phenomena 'traceable' in the brain?
Preface

Your question can be phrased as: what controls storage of information in Long-Term Memory? And more specifically, declarative memory? And one answer to this is one of my favourite stories in neuroscience.

In the following, I'm ignoring a lot of important aspects about memory - especially the difference between encoding, consolidation and retrieval. But I hope it still answers the question.

Psychology of memory

We generally distinguish between two forms of memory. Procedural memory is about sequential, a-then-b type of stuff - for example, movement patterns, like dancing, or calligraphy. There's basically only one way to get stuff into procedural memory: grind it in there. Do it a lot. Do it so much, it stops being under conscious control, and submerges into cerebellum and motor cortex. This is so for everyone; even the people who're absolutely the best at some sport or instrument will practice day after day after day to really get it down, to effortless perfection.

The other kind is declarative memory. This is a-is-b memory; the three branches of government are judiciary, legislative and executive, and the dorsal stream is where and the ventral stream is what, and your wedding anniversary is on 11.9. and so on. In contrast to procedural memory, declarative memory is conscious and controlled, it's largely subserved by different brain areas, and it is acquired in a much different way.
If you want to learn to rumba, you got to learn to rumba a lot. But when you're at the [book store/nightclub/sports venue] and the most attractive [boy/girl] you've ever seen walks by, and up to their friends, and is greeted with "Hi Alex!", you'll immediately store that name. You won't have to listen to the friends say "AlexAlexAlexAlexAlex" again and again. You'll hear it once, and remember it immediately, and possibly forever. 
This is because you're aroused.
Roughly the same thing happens if you eat something and get extremely sick afterwards, or if you get a shock after pushing one lever, and a treat after pushing the other. Why? Your arousal - be it positive, or negative - is high. Metaphorically speaking, your brain thinks "whatever is going on right now seems to be important, I better store what's going on". 

One cool experiment in that regard I can't find the citation for right now goes like this: students saw either a neutral video, or a disgusting surgery video after the lecture. A few weeks later, those students who had seen the surgery video did significantly better on those questions of the exam relating to the lecture after which they'd been shown the video. Another example is how so many people know what exactly they were doing on 9/11, when they heard the news. Do you remember what you did two days before? 7? But 9/11 was uniquely arousing.

The reverse is, of course, that we don't remember boring stuff. You remember Alex' name, but not their 7 homely friends' names. You remember every detail of Star Wars: Empire Strikes Back, but not your math classes - or a boring movie (what was the plot of Star Wars Episode 2?). And why would they? Evolutionary speaking, there is very little point to storing memory about low-arousal situations; if they had been important, they would have been arousing, right? Memory formation is costly, so we only do it when we (think we) have to.

Individual differences

And that's the gist of it, really: low-arousal situations are not conductive to declarative LTM formation. And the stuff we study is very often low arousal.
Now to get it right, there are two options. The first is: be aroused! If you truly care about math, you will remember this stuff. It will be much easier to memorize information you actually care about. And this is one way by which people differ: some are more, some less bored by abstract, complicated information.

The next one is that our ability to focus obviously differs. Some people have short attention spans, some longer attention spans. A bit simpler than your question about salience, simply paying attention vs. not paying attention makes a huge difference, and some people are much better at paying attention to boring stuff than others. These people are often much better at reading something boring again and again. Because the situation is low-arousal, chances of encoding are still bad, but better than when you don't look at it, and eventually, it'll get there via mere exposure.

That is, then, my answer: two main factors concerning inter-individual differences in declarative LTM formation are 1. different propensity to find abstract, complex information interesting/boring, 2. different ability to study even though something is boring.

Neurological substrate

Surprisingly, the neurophysiology of this is relatively well understood. "[E]ntry of information into long-term memory", as the title of Lisman &amp; Grace's paper goes, is mostly controlled by two sets of brain structures: an interaction between the medial temporal structures, especially the hippocampus, that controls the encoding of memories, and the mostly subcortical systems signaling salience and valence of events. The neighboring amygdala as the coder of valence, and, most importantly, the subcortical VTA (dopamine source) and the Locus Coeruleus (norepinephrine source) tell the hippocampus to "open its gates" for declarative memory formation in arousing contexts, to arousing stimuli. These systems are of course also generally relevant for setting the "tone" of the brain - from aroused to lethargic; this is under the control of the Locus Coeruleus. So, what's out there - arousing, novel, salient stuff? Dopamine/Norepinephrine up, hippocampus "gate" open, declarative memory in. Boring situation? Dopamine/Norepinephrine down, hippocampus shut.

You can still learn to rumba though. Just do it a lot. You don't need the hippocampus for that (as HM's ability to acquire new motor patterns shows).

Some references

Neurophysiology

Lisman &amp; Grace, Hippocampus-VTA Loop/Dopamine

One specific experiment showing Dopamine is crucial for LTM persistence

Sara &amp; Bouret, Locus Coeruleus/Norepinephrine

Psychology

Arousal and memory

Single-exposure rich memory formation for arousing events

And another one, for 9/11