If there are huge gaps between atoms relatively to their size, why can we touch things? Most of the volume of an object actually consists of empty space rather than molecules. So why don’t solid objects move through each other?
 A: 
Most of the volume of an object actually consists of empty space

Although this is frequently stated and frequently believed, it is false. The space in an object is not empty but is filled with many strong fields. Since everything, including matter, consists of fields, a region that is so filled with strong fields cannot justifiably be called empty.
What is more interesting is the presence of many fermionic fields which prevent multiple excitations sharing the same state. These fields cannot pass through or stack on top of each other as bosonic fields like the photon field. This is an important key for understanding how some fields feel substabtial while others don’t.
A: The reason is that there is a force called electromagnetism that prevents atoms and molecules from going through each other.
Whenever you touch something, your hand does not go through because of this force. Upon contact, your hand and the table (let's say) do not pass through each other because the electromagnetic force repels your hand from the table and the table from your hand.
Even though atoms are mostly empty space, the electromagnetic force has a greater influence than the individual particles that make up the atom. The electrons surrounding the atoms of the table interact with the electrons of your hand via the electromagnetic force.
Since electrons have the same charge, and like charges repel, that means your hand cannot go through the table because of this.


See

*

*https://en.wikipedia.org/wiki/Coulomb%27s_law

*https://en.wikipedia.org/wiki/Quantum_electrodynamics

*https://youtu.be/X-FEU4mQWtE?t=7
A: A very short answer is "Objects do not move through each other due to electromagnetic forces". Like charges repel, opposite attract. When you bring two atoms close together the electromagnetic force $F=k\frac{q_1q_2}{r^2}$ increase (since we decrease the distance $r$).
