Pure Substance
A pure substance is matter with a fixed composition and uniform properties throughout; every element and every compound is a pure substance.
Definition
A pure substance is made of only one kind of thing all the way through, either a single element or a single compound. It has a definite, constant composition and a fixed set of physical properties such as melting point, boiling point, and density, and it cannot be separated into other substances by physical means such as filtering, evaporating, or distilling. Thermodynamically, a pure substance shows sharp phase transitions at fixed temperatures for a given pressure, unlike mixtures, which change phase over a range. Absolute purity is an idealization: laboratory grades are specified by impurity limits, and separation methods such as distillation, recrystallization, and chromatography approach but never reach $100\%$.
Example
Distilled water is a pure substance because it is all $H_2O$, and a copper wire is a pure substance because it is all copper atoms. Pure water freezes at exactly $0^\circ\text{C}$ and boils at exactly $100^\circ\text{C}$ at sea level, while salt water, a mixture, freezes below $0^\circ\text{C}$ and boils above $100^\circ\text{C}$, with the exact values depending on how much salt is present. Semiconductor-grade silicon must be at least $99.9999999\%$ pure (nine nines) because even one boron atom per billion silicon atoms measurably changes its electrical conductivity, and that purity is reached by repeated zone refining.
Key Insight
In science, "pure" does not mean clean or healthy; it means one substance only, so pure chlorine gas is pure even though it is poisonous. A sharp, fixed melting point is a quick test for purity, since impurities broaden and lower the melting range, which is why chemists check melting points to confirm they made the right product. Even "pure" tap water is a solution of dissolved minerals and gases, and even distilled water contains $H^+$ and $OH^-$ ions from self-ionization, so purity is a matter of degree and the real question is whether the impurity matters for the use at hand.