What is the Difference between using root motion and not?When should we use it?

Animations can be authored including root motion or without root motion.
A walking animation without root motion will simply walk on the spot. This is called Game Driven motion where you decide how fast the character is moving and play the correct animation to match. This is what the ThirdPersonCharacter does when you create a basic blueprint example project. It has a walk and a run animation and uses a blendspace to decide which one to play depending on what speed your character is moving at.
The downside is that you can end up with a character moving but the amount of times the feet touch the ground don’t match the speed perfectly so the character can seem to float along.

A walking animation including root motion includes how far the character should be moving forwards for each frame of the animation. The root node contains the information about how far the character should translate - hence root motion.
This is called Animation Driven motion and the animation that you play determines how far you travel. It gives you motion that should perfectly match the distance covered and get rid of that floating effect if you implement it properly.

A useful overview summary of the two is in the following video (starts about 5 mins into video.)

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