Part of it is the imperfection of human nature amplified by the imperfections of society. In an ideal world, the answer to the casual question "What are you currently working on?" would be "I'm currently stuck on this particular lemma" followed by the formulation a decent graduate student working in the field would easily understand. Then it would be your turn to channel the conversation into various ways from "What do you want to use it for?" to "What partial cases can you solve?" to "What techniques have you tried and where is the difficulty" to... depending on how good/bad your erudition, understanding of the subject, technical skills, and the ability to think on the fly of a new topic are.
The imperfection of the human nature is that one often wants to make a good impression more than to convey the information, so one starts with some "big" picture he believes his work fits in and tries to justify the importance of his project and, in the worst case scenarrio, of himself too. It takes some courage to openly declare that no human being and/or project have any particular importance or value in the grand design of this Universe, so we'd better drop all pretense and just try to cooperate in the most efficient ways to achieve something before our time as individuals or species runs up. One often perceives the question "What are you doing?" as "How can you justify your existence?" and tries to answer that instead as if the asking person were a prosecutor on the Last Judgement.
The society imperfections amplify this in several ways. First, there is an objective problem of allocating limited resources to competing individuals. This leads to direct comparisons of really incomparable things and, since no really meaningful comparison can be made (or, rather, too many justifiable comparisons exist with contradicting results), the pseudo-measures like "importance", "general interest", and many others abound. The worst case scenario is that they are measured on scale from 0 to 10 and the points are then added up with some fancy weights. There is nothing one can do about it until the supply exceeds the demand (which is not going to happen soon), so one is constantly kept on guard in academia and elsewhere as to how he is going to present his work, where to submit his papers, what to do to get good student evaluations, etc. This insecure feeling may easily extend to the cases where there is absolutely nothing to fear of, hide, or fight over, like casual conversations about science. However, this is only half-evil because this insecurity can also serve as a drive to do something instead of lying on the sofa and spitting at the ceiling.
The real "root of all evil" is the oxymoronic expression "intellectual property" and the whole convoluted culture around it. Some people will never openly tell you what they are really working on just because they are afraid that you may "steal their ideas" (as if an idea, by its very nature, were not a subject for sharing to the extent that sharing it is the only way to support its very existence), or may "want some share of credit", or for other equally non-sensical reasons (IMHO). This is how many people perceive it even if their scientific reputation is beyond any need to defend at each corner. It also gets reflected even in popular publications about science. I recall the passage about Andrew Wiles somewhere, the sense of which was "Now he had a difficult task to find a person who would be able to help to fix the gap but not take the whole credit for the proof" (Richard Taylor). The NY Times article puts it less bluntly but you'll easily see that the underlying meaning is there. This creates extremely distorted attitudes towards the meaning of the whole endeavor (again, IMHO), which are rather widespread.
At last, there are fashions. You have as many people who want to boast about working in fashionable fields as those who want to wear fashionable dresses and haircuts. That usually is responsible for various "buzzwords" in introductions to mathematical articles or on hiring committee discussions (currently it is "big data", before that we had "mathematical biology" and "nano-science", I'm not trying to predict what comes next) and can spill even into casual conversations when two people are sniffing each other for the first time. As any fashions, the mathematical ones may make sense or make no sense, but they are all destined to come and go. Unfortunately, we'll see the distilled product our generation of mathematicians produced only 50-100 years later, which is beyond the lifespan for most of us.
So, I would say, make nothing of that conversation except the usual conclusion that when you are asked the same question, try not to behave in the way you disliked. I'm not saying "Try to be always straight and honest": if you ever write a grant proposal, prepare a file for promotion, or try to convince other members of the hiring committee that your candidate is "the best", you'll find that this is plainly impossible in this world if you want to get something more than to preserve your "integrity" (the latter is possible in principle but the price is the one Grisha Perelman paid and there was a lot of misunderstanding there on both sides as far as I can tell). Just try to impose some limits on stretching your conscience and look at the mirror now and then before judging others too hard (I certainly will plead guilty myself to whatever "crime" I described in this long rant if somebody wants to bring the charges).