The primary characteristic of a compound is that it has at least two different types of atoms, and that these atoms are always present in the same ratio. For example, table salt is formed when one atom of sodium combines with one chlorine atom, and all compounds of sodium have the same 1-1 ratio. Additionally, compounds can cause the characteristics of the individual elements to change; pure sodium (which does not exist naturally) is highly flammable in water, but when combined with chlorine, it harmlessly dissolves.
In the structure of an atom, electrons orbit around the nucleus, which contain the protons and neutrons. When a compound is formed, electrons from the outer shell of one type of atom are donated to the outer shell of a different type of atom in what is known as a "bond." There are two types of bonds: "ionic" bonds, which involved ionized versions of atoms (e.g., atoms that are not neutral in charge), and "covalent" bonds, which involve only neutral atoms.
Compounds are expressed in the format known as a chemical formula. Chemical formulas use the abbreviations from the periodic table of elements, and they show the ratio of atoms needed for the compound for form. For example, sodium chloride is expressed as NaCl, as "Na" is the abbreviation for sodium (taken from its Latin name, "natrium") and "Cl" is the abbreviation for chlorine. H2O is water, and this indicates that two hydrogen atoms and an oxygen atom make water, and only in that ratio (in contrast, H2O2 forms hydrogen peroxide).
A molecule is a combination of any two atoms, and thus includes things like H2 (hydrogen gas), which is not a compound because it is not two different types of atoms. All compounds are molecules, but not all molecules are compounds; indeed, the term is often used interchangeably, and the smallest portion of compounds are referred to as molecules (e.g., H2O is commonly referred to as a molecule of water).