Kiasu means 'afraid of losing' if directly translate from the original word. It's not a proper English but it is translated from Chinese Hokkien dialect. It reflects how competitive a society can be.
"Eh, why you so kiasu? Everything also want, everything also want to win!"
Sometimes, as simple as queuing up for buying concert tickets as early as 5am in the morning, or even camp at night outside the ticket selling area, when tickets are only up for sale 10am the next day! This, to me is also an act of kiasu.
As I am still a university student, I find students who are competitive, kiasu. They are normally those who get top grades in class. Some of them might even peek at your notes what you have written down during lectures, that he/she might left out. (That is a not a big deal for me of those student who do that) The most kiasu students are those who kept telling you they have not finished their reading before exam when actually they already prepare for it. In the end, they score really well. However, all these kiasu situation can have its brighter side that it helps one to improve and excel in their own way.
Keep that aside, in general public, many people, I would say Asian in particular, very kiasu, not only in their act as well as during conversation. Whenever you said something, they think of that they cannot loose their dignity and think of a lie or something without realising for you to know that they are better than you. Though sometimes I am quiet, I scrutinise. I am quite good in observing other people or things in my surrounding. Sometimes, give and take, is all it needs for a good conversation, be truthful and not too kiasu. Listen, observe and talk. Sometimes, I think 'dua-pao' is equivalent to kiasu in certain conversation. (For those who dont understand hokkien, ask me what 'dua-pao' means.)
I trust that, there's a kiasu character in each and everyone. It all depends on how you surpass the brighter side of kiasu-ness. Parents can be kiasu, too, to find the best school for their kid, in order for their children to be a intelligent, better than the kids next door. You can either be kiasu while dealing with business, conversation, studies or anything without realising.
Here's a comic for you to enjoy, adapted from Google Images.