When most people think of core training they think of crunches and sit-ups. While these exercises do engage the abdominals when performed correctly, they aren’t a very functional movement and therefore the strength gained from such exercises will not efficiently translate to improved performance in athletics or in day to day activities. Lying floor exercises have there place in a workout but it should be as part of a well-rounded routine that includes compound strength exercises and core stability isolation exercises.
Core stability exercises are exercises that work our entire core without any movement in it (flexion or extension). In other words, the workout comes from keeping your core tight to maintain a neutral spine position against resistance. The most basic example of this is the plank exercise but that is only the tip of an iceberg worth of progressions.