Is it important, and why? I heard it helps you stabilize the shoulderblades but I don't get it.
Stretching the fingers and keeping your entire hand actively pressed against the floor helps to distribute the pressure away from your wrist. Experiment with some planks, where you first think about pressing the entire palm and fingers against the floor, making as much contact as possible, and then try relaxing and even lifting your fingers off the floor, so the weight is concentrated in the heels of your hands. For some folks, this is painful, so certain hand placements are safer.
But what if you want to strengthen your wrists and fingers? I don't think anybody would tell Bruce Lee to spread his hands. Fingertip pushups, kettlebell pushups, and other variants (Here's a fun list) are designed to create instability so you work different muscle groups. They are perfectly valid exercises where the cue to spread hands is meaningless, and yet stability still matters.
Regarding scapular stability, my guess (just a guess) is that you heard that because someone thinks that a person who is spreading their hands will naturally flex and stabilize other parts of their body. Like if you were to clench your fists without thinking too much, do you also flex your biceps, pecs, or abs a little? And if you think a little more about it, is it possible to clench your fists without also flexing those other muscles? Scapular stability is similar. You need it, but you need body awareness and actual upper back strength in order to have real scapular stability.
Last link: here's a guy with a pretty solid push up, and his hands look relatively relaxed against the floor.