There are two components to martial arts training: the development of attributes and the development of skills. Attributes include physical qualities such as flexibility, strength and endurance. Skills include learned motor movements like kicking and punching. The development of skills will be severely limited if the development of attributes is neglected. However, attributes can easily be developed exclusive of skills. Of course developing attributes without skills falls into the realm of calisthenics, not martial arts.
In the early stages of learning a martial art, the practice of skills alone may serve to develop a wide range of attributes including flexibility, strength, coordination, reflexes and endurance. As you become more adept and your physical condition improves, you may have to develop certain attributes independent of skill practice by devoting time each training period specifically to conditioning exercises.
For example, when you first learn a front kick you may progress rapidly in the technical development and performance of the kick up to chest height. At some point, you will want to kick harder, higher or faster but cannot seem to make any further gains through practice of the kick alone. At this juncture, the addition of flexibility or strengthening exercises for your legs will directly contribute to the further development of your kicking skills.
Similarly, when you first begin taking martial arts lessons, the strenuousness of class itself may be enough to give you a good cardio workout. As your cardiovascular capacity improves, class will begin to seem easy and you may find the need to supplement your class time with additional cardio workouts such as jogging or cycling.
Conversely, you may find that your attribute development is hindering your skill development if your conditioning plan is not specifically designed for martial arts. If you are running nearly fifty miles a week for cardiovascular conditioning, you may find that the speed of your kicks suffers because you are developing endurance related slow twitch muscle fibers in your legs rather than the more explosive fast twitch muscle fibers.