Subatomic particles are the building blocks of atoms. They include protons, neutrons and electrons. Protons and neutrons are located in the nucleus of the atom and the electrons are located on shells that surround the nucleus.
Valance electrons are the electrons on the outermost shell of an atom, the valance shell.
Each shell that surrounds the nucleus can only hold up to a certain number of electrons. For example, the first shell, the shell closest to the nucleus, can only hold up to 2 electrons. The second shell can hold up to 8 electrons and this is the same with the third shell.
Atoms can have a different number of shells. For example, hydrogen atoms have 1 shell that has 1 electron. Fluorine atoms have 2 shells with 2 electrons on the first shell and 7 electrons on the second.
The octet rule states that atoms prefer to have a full valance shell, meaning that the number of valance electrons on its outermost shell is maxed out. For example, hydrogen would prefer to gain 1 electron and have 2 electrons on its valance shell, since it only has 1 shell and the first shell only needs 2 to be maxed out. Fluorine would prefer to gain 1 electron and have 8 electrons on its valance shell since it has 2 shells and the second shell needs 8 electrons to be maxed out.
I hope this helps!