Though most games track the total deaths or kills a player gets for the purpose of stat-tracking and awarding achievements, most gamers would rather know their KDR (obviously, kill-to-death ratio) as it provides several advantages over a block summary of the two.
It is easier to read into a KDR's meaning. Getting 70 kills and 60 deaths means very different things depending on what game you play. With a KDR there are three primary states: less than 1 to 1, 1 to 1, and more than 1 to 1. If your KDR is less than 1 to 1, you are being outmatched; if you get 1 to 1, your skill is comparable to those around you; if you are over 1 to 1, you are doing better than the average player on the server. These principles never change unless circumstances suggest that you should have a particularly high or low KDR, such as a mode where certain players possess capabilities the others do not, or where a player's primary goal is not to kill the opponent but rather to complete an objective. In these cases, KDR becomes a less useful statistic.
KDR is very informative on a case-by-case basis. Because the KDR of your enemies and friends in any match are all interrelated in a "1 kill-for-them, 1 death-for-you" exchange, KDR is always relative to a particular set of people. The average of everyone on the server always equals 1 to 1, which is why having a 1 to 1 always means that your skill is average in the current setup. Armed with this info a player can play a bit, assess their capabilities against those around them, and stay if he or she finds the other players to be worthwhile competition (or if he or she is vastly superior to their competition, in which case they stay on because they're pricks). This idea is not universally accepted, but can be helpful for individuals who want to be sure they aren't deluding themselves about their own abilities.