Round corners give shapes a softer, more modern look — they feel friendlier than sharp edges.
Steps to round corners of shapes
Select your shape layer. Twirl down Contents → Rectangle → Rectangle Path.

Adjust the Roundness value to smooth out the corners however much you want.

One more thing
Animate Roundness with keyframes for fun morphs between sharp and soft edges — it creates a really nice visual effect.
Related how-tos
How to animate a mask path in After Effects
How to create a rectangle mask in After Effects
How to create shape layers in After Effects
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