Spyro has a limited number of lives that he can make use of. If he loses all of them, the game will end. You can avoid such a situation by accumulating additional lives. There are two mechanisms for this.
The first of these is the destruction of something that resembles a turtle in shape. These objects can be found on almost every map. Destroying it will automatically give you an extra life. These objects are disposable. This means that they no longer appear on the map after you use them.
The second option is to collect small orbs dropping from enemies. You can only gain them from enemies who have been defeated before. That's why starting locations are a good source of them, as you have to explore them several times. When you move through them to the next level, you can, by the way, liquidate all enemies in the area again. One such orb is just a small fraction of your whole life bar, so you need to collect the right amount of them.