Motion blur makes fast movement look natural instead of stiff. It’s the difference between something looking smooth and something looking like it was shot frame-by-frame.
Steps to add motion blur
Toggle the Motion Blur switch (the three circles icon) on your layer in the timeline.

The toggle at the top of the timeline activates automatically, but if it doesn’t, turn it on yourself.

Preview your comp — fast-moving layers now blur automatically as they move.

One more thing
If it looks too soft or not soft enough, increase the Shutter Angle in Composition Settings → Advanced. That controls how much blur gets applied.
Related how-tos
How to add keyframes in After Effects
How to use easing for smooth animation in After Effects
How to fade in and fade out layers in After Effects
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