the earth is actually not perfectly round, it is called an ‘oblate spheroid’ the diameter of the earth is wider around the equator due to the rotation of the earth and its non-solid insides being pushed outwards
generally though its because gravity acts equally in all directions, and the most efficient shape in terms of volume versus surface area is a sphere, when objects in space become planet sized, they tend to become round as they have enough gravity to squash themselves into a round shape!
As Simon says gravity acts the same in all directions. If you were allowed to turn around but not to move, you would be able to reach the same distance in every direction (the length of your arm). If you whirled around you would trace our a spherical shape. Just like your arms, gravity’s reach extends the same in all directions.
All I can add is that the Earth tries hard to keep the same shape, even when things change on the surface. There is a recent theory that suggests that if an object of sufficient weight on Earth — for example, a supersized volcano or the continents collecting together — formed far from Earth’s equator, the force of Earth’s rotation would gradually pull the object away from the Earth’s rotation axis back towards the equator.
And to add to all these great answers, another name for the shape of the Earth is “Geoid”, and has by some scientists been compared to a really big potato…
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