Final answer:
Gravity is a built-in feature of mass which continually acts to attract objects possessing mass towards each other, weakening with distance but never reaching zero. The Earth spins due to conserved angular momentum, and gravitational attraction is balanced by celestial bodies' motion. Gravitational repulsion does not exist in the current understanding of physics.
Step-by-step explanation:
Gravity exists as a fundamental property of mass. Every object with mass has an attraction to other masses, which is the basis for the law of universal gravitation described by Sir Isaac Newton. The force of gravity not only keeps planets in orbit but is also why you don't fall through the Earth when you jump. Although gravity weakens with distance, it never actually reaches zero.
The Earth keeps on spinning due to its initial formation and angular momentum conserved from the time when our solar system was a spinning disk of dust and gas. The Moon doesn't crash into Earth because it is in orbit, with its forward motion balancing the inward pull of Earth's gravity. Similarly, when an ice skater pulls her arms in, she's conserving her angular momentum, which makes her spin faster without additional external torque.
There isn't a phenomenon known as gravitational repulsion; gravity always attracts. The energy for gravity doesn't 'emerge' from anywhere; it is an intrinsic property of matter resulting from the curvature of space-time according to Einstein's theory of General Relativity.