Whether an element exists as separate atoms or as bonded molecules depends on its electron configuration. The six noble gases, helium, neon, argon, krypton, xenon, and radon, already have a full outer shell of electrons. This makes them extremely unreactive, so they exist as individual, unbonded atoms under normal conditions.
Most other elements are not so lucky. Their atoms have incomplete outer shells, so they bond with themselves or other elements to become more stable. This is why elements like nitrogen and oxygen form diatomic molecules, N2 and O2, rather than floating around as single atoms.
Elements like sulfur and phosphorus form even larger clusters for the same reason. The monatomic idea also applies to ions, not just neutral atoms. A monatomic ion is a single atom that has gained or lost electrons to gain a net charge.
Examples include sodium, Na+, and chloride, Cl-. These ions remain single atoms even though they carry a charge. This distinguishes them from polyatomic ions like sulfate, SO4 2-.
A polyatomic ion contains multiple bonded atoms that share one overall charge. A common misconception is that noble gases can never form compounds at all. Under special laboratory conditions, heavier noble gases like xenon can be forced to bond with highly reactive elements like fluorine. This is rare and does not happen under normal, everyday conditions.