Muscular endurance, sometimes called muscular respiration, is the ability for a muscle to repeat a specific movement repeatedly. This is dependent on the body's ability to supply the muscle with oxygen, so it is obviously dependent on cardiovascular fitness. However it also depends on the muscle's ability to utilize the oxygen efficiently.
At the muscle site oxygen must be able to enter the muscle cells in sufficient amounts. The muscle cells be able to utilize this oxygen quickly and efficiently in order to produce energy.
Developing significant muscular endurance is difficult and requires many years of training. That's why most endurance athletes, such as marathon runners, are older. It is very odd to see a 20 year professional marathon runner, or endurance cyclist. Mitochondria are little units in muscle cells which are responsible for oxygen/energy production. And it takes years to increase the number of mitochondria and to make them more efficient.
In addition to training, genetics and muscle type are the two major factors that can affect muscular endurance.
Many times the fatique that an athlete might experience may not be from cardiovascular limitations but rather from muscular respiration. For example, if you are running and your legs feel very tired, but you are not breathing hard then chances are the limiting factor is muscular as opposed to vascular.
It used to be thought that you can only improve cardiovascular fitness and muscular endurance only by performing continuous activity, e.g. running for 30 minutes. Now we know that this is not true. In fact, interval training can provide higher stress on the body and therefore lead to greater improvements. By interval training we are referring to an exercise which has rest periods. This can be done with running, hill climbing, swimming, cycling, rowing, and even weight lifting, etc. The idea is to work hard (harder than you would in a continuous activity) for a time period, then resting for a time period. The best ratio for this is usually a work to rest ratio of 1:2. E.g. run for one minute, rest (walk slowly) for 2 minutes. And repeat this 5-6 times.
If you are going to do interval training then you should try to get your heart rate to about 85% of its maximum during the exertion phase. When you are in the recovery phase try not to let your heart rate go lower than 60% of its maximum before doing the next work phase.
Interval training is a bit harder on your body so make sure you are generally fit before trying it.