an electron shell
Picture the electrons around an atom not as a jumble but as seated in a set of nested arenas, like the rings of seats in a stadium: the innermost ring fills first and sits closest to the stage (the nucleus), and only when it is full do electrons take seats in the next ring out. Each ring is an electron shell, a band of allowed energy levels a certain distance from the nucleus.
Shells are labelled n = 1, 2, 3, and so on outward, and each holds a limited number of electrons: up to 2 in the first shell, 8 in the second, 18 in the third (the pattern is 2 n^2). Inner shells sit at lower energy and are held tightly; outer shells are higher in energy and more loosely bound. Sodium, for example, has 11 electrons arranged 2, 8, 1: two shells filled and a single lonely electron starting a third. That lone outer electron is the reason sodium is so reactive.
Shells are the bridge from the atom to chemistry, because only the outermost shell touches the neighbours. A filled outer shell is unusually stable (this is what the noble gases enjoy), so atoms gain, lose, or share electrons to reach that comfortable full-shell condition, and that drive is exactly what forms bonds. The neat cartoon of 2, 8, 8 shells is a simplification of the true quantum picture of subshells (s, p, d, f), but it predicts bonding behaviour remarkably well for the light elements.
Chlorine has 17 electrons in shells 2, 8, 7, one electron short of a full outer shell of 8. Grab one more electron and it becomes the very stable chloride ion Cl^-. That single missing seat is why chlorine so eagerly bonds, for instance snatching sodium's lone outer electron to make table salt.
The outer shell's fullness decides how, and how eagerly, an atom bonds.
The 2, 8, 8 filling rule is a beginner-friendly shorthand. The real ordering (from quantum subshells) has exceptions even early on: the fourth shell begins filling before the third is finished, for instance, so treat shell counts as a guide, not an iron law.