It’s all due to the anaerobic system coming into play when the aerobic system cannot deliver enough energy. And it hurts, because the anaerobic system leaves waste products in the muscles, which hurt.
Anaerobic means "without oxygen". During anaerobic work, involving maximum effort, the body is working so hard that the demands for oxygen and fuel exceed the rate of supply. Waste products accumulate, the chief one being lactic acid. The muscles, being starved of oxygen, take the body into a state known as “oxygen debt”. The body's stored fuel soon runs out and activity ceases, painfully. Once into oxygen debt, it takes only a few seconds at maximum effort for the fuel stored in the muscles to run out. Fortunately the body can resume limited activity after even only a small proportion of the oxygen debt has been repaid.
What can we do to overcome this? We can train the body to get rid of lactic acid more efficiently, to handle higher intensities, and to run at a higher heart rate, all of which means we can train to run continuously at a faster pace. To achieve this, setting out on regular training runs at “threshold intensity” is the best approach for Masters athletes. On some of your longish runs, pick the pace up for just a few minutes at a time, rest for a bit then repeat. You want to find out where your anaerobic threshold is: the point at which lactic acid is being removed at the same rate it is being formed. The “talk test” comes into play here. Most training is aerobic and you can talk; at the anaerobic threshold you can just about talk but with few words at a time; beyond the anaerobic threshold you can hardly talk at all!
The other approach is to do specific anaerobic workouts, such as very fast intervals of between 100m and 400m with a very short recovery in between, just enough recovery to get your breath back. These are risky because they are so exhausting. And after such a session, racing or speed-work shouldn’t recur for 3 or 4 days, even for the fittest athletes. So these days, I don’t recommend this kind of intense session for Masters. There are plenty of effective alternatives which are kinder to our bodies.