The table is not a list — it is a graph. Pick a property and walk across a period or down a group, and the same shapes keep reappearing. That repetition is what "periodic" means.
Atoms get smaller left to right — the nucleus gains protons and pulls the same shell in tighter — and bigger down a group, because each period adds a whole new shell.
The energy needed to strip one electron. It climbs across a period and falls down a group, for exactly the opposite reason radius does: outer electrons get further from the nucleus and easier to remove.
How hard an atom pulls on shared electrons. Fluorine is the champion at 3.98; caesium and francium barely pull at all. This single number predicts whether a bond is ionic or covalent.
Metals give electrons away, non-metals take them. The staircase of metalloids — B, Si, Ge, As, Sb, Te — marks the border, and those in-between elements are exactly the ones that make semiconductors.