Latency is the waiting time. It is the gap between clicking a button and the screen responding, or between a sale at the till and the stock figure changing elsewhere. It is usually measured in fractions of a second, but even small delays feel long when you are serving a queue.
Low latency matters where people are waiting on the system, such as at a busy counter, or where several sites rely on the same live information. Causes include distance to the server, a slow connection, or heavy processing behind the scenes. Techniques such as caching can reduce it, and so can simply choosing sensible hosting.