Classical physics is an approximation to reality, but it works just fine for everyday use. For the most part, the world is made up of three kinds of point particles: electrons, protons, and neutrons.
All of these particles attract each other with a weak gravitational force.
There are also much stronger electrical forces. Electrons repel electrons. Protons repel protons. Electrons and protons attract each other. When electrons and protons move, there are also magnetic forces. Neutrons are not affected by electric forces, and have a very weak response to magnetic forces.
There are also two more forces: The strong and weak nuclear forces. For the most part these are ignored. They make protons and neutrons attract each other when extremely close together and stick to each other in atomic nuclei. Other than this, these forces are mostly ignored in classical physics.
There is also light. Light is an electromagnetic wave, an electric/magnetic field that varies in time and space.
For the most part, that is the world of classical physics. There is more, but when people talk about it, they usually get into better approximations of reality like relativity and quantum mechanics.
Classical physics doesn't explain why there are forces. They just are. It explains in detail how forces affect particles, and how particles and their motion affect the forces.
One important thing about these forces is they occur between pairs of particles. If particle A exerts a force on Particle B, then Particle B always exerts an equal and opposite force on particle A.
Explanations are simpler when speeds are much much slower than light, and this suffices for your question. Forces are simple attractions and repulsions. All the particles in you are gravitationally attracted to all the particles in the Earth. Since there are a lot of particles in the Earth, this weak gravitational for adds up.
There are more complex forces between atoms, where there is both attraction and repulsion at the same time. It takes quantum mechanics to explain it correctly. In classical physics, we just say there are atomic bonds. Atoms exert strong forces on each other that keep two atoms a fixed distance apart. It also keeps angles between atoms fixed.
This makes rigid bodies possible. Very large collections of atoms stick together, where each atom has a fixed place. If you push on an atom at the surface of such and object, the surface atom pushes on its neighbors to keep them the proper distance away and at the proper angle. The neighbor atoms push on their neighbors and so on. The net result is the entire rigid body is pushed without deforming it.
There are also bonds that result in liquids and gasses. And more complicated things like you and me. We are partially solid and partially liquid, and not all that rigid unless we tense our muscles.
When you stand on the floor, you would fall toward the center of the Earth, except that the floor pushes upward on the soles of your feet hard enough to keep you still. When you stand, you are rigid enough that neighboring atoms push on each other and keep all the atoms in you in their proper place. You don't fall to the floor like you would if you relaxed.
When you lift one foot off the floor, the same thing keeps you upright, except that the forces between neighboring atoms are different. All the upward force from the floor is under just one foot. But still, the atoms at the bottom of that foot push upward hard enough to keep their neighbors in their place. Those atoms push on their neighbors and so on. All the atoms in you stay in their places because of forces from neighboring atoms. Now the forces in your uplifted knee are attracting atoms below them so your leg doesn't fall off.