Historically, a point has been described as an exact location in a space, with no length, width, or thickness.
In modern mathematics, a point refers more generally to an element of some set called a space. Therefore, the mathematical definition of the point has become abstract, with no specific physical features unless defined.
In physics, a pointlike particle is an idealization that follows the former definition of having no length, width, or thickness. Abstractly, any object in the universe appears to vanish to a point when viewed on large enough scales.
This fact, coupled to the mathematical definition given above, leads to many possibilities in terms of pointlike particles, including the conception of planets, stars, and galaxies as “points.”