So far, Sweek Nell Fenwick and Canaday are closest to the way I understand the reason for training at "lactate threshold". I'd like to add a few things.
I prefer an older term, Onset of Blood Lactate Accumulation. I like this term becasue, as already mentioned, lactate is always being produced. It's just that as we run faster, the lactate builds up faster than our bodies are able to clear it from the tissues/bloodstream.
Whether OBLA is a CAUSE of fatigue (as is generally accepted by coaches and runners) or whether it simply a MARKER of fatigue (as explained by the Central Governer Model) is irrelevant.
Training at ANY intensity will give a training effect, provided you do it long enough to provide physiological stress to any one of the body's systems responsible for running performance (circulatory, musculoskeletal, nervous, respiratory). The HARDER you work, the GREATER the stimulus. However, the stimulus must be applied for an extended period of time in order to create a response. This is why we don't just run all out 100m sprints every day in training.
In 1981, MacDougal and Sale conducted a meta-analysis of over 75 previous studies on training intensities' influence on oxygen consumption and concluded that TISSUE HYPOXIA was the most important stimulus for development of a large number of the physiological variables that allow the body to use oxygen efficiently (capillarization, mitochondria density, myoglobin concentration, aerobic enzyme function). It just so happens that the intensity that brings about OBLA corresponds to a very hypoxic state. You could run harder, but your muscles wouldn't get any more hypoxic.
So, here is why training at intensities that bring about OBLA, or slightly less intensly, is important. As S.Canaday said, you get more "bang for your buck" . You can run at LT, or OBLA or whatever you want to call it for a relatively long time. You can keep your muscle tissue hypoxic for a relatively long time. You can apply a stimulus which has been shown to increase many important physiological variables for A RELATIVELY LONG TIME without becoming overly fatigued.
There is an old axiom among the coaching ranks: Training Load = Training Frequency (F) X Training Intensity (I) X Time (T). One of my old coaching manuals called it the FIT principle. OBLA represents a relatively high intensity that can be done for a relatively long time. If you followed the training of Marius Bakken when he was in his prime, you could see that it can also be done with a great frequency. Here is an article from back in the stone age (2000) by a very accomplished coach describing his athletes training at OBLA with a very high frequency
http://www.coacheseducation.com/xc/jack_farrell_july_00.php
He never uses the terms OBLA or LT, but he is precisely describing the intensity. The author of the above article was the coach of Kim Mortensen, who still holds the girls national record for 3200m