mole fraction
Picture a crowd at a party. The mole fraction of any one type of guest is just the share they make up of the whole crowd — if 1 in 4 people are wearing red, red's "fraction" is 0.25. In a solution, the guests are molecules; the mole fraction of a component is the number of its molecules divided by the total number of all molecules present.
Formally, the mole fraction of a substance (often written x) equals the moles of that substance divided by the total moles in the mixture. Because every component's share is part of the same whole, all the mole fractions in a mixture add up to exactly 1. A mole fraction has no units — it is a pure ratio of counts, like a percentage written as a decimal.
Mole fractions are the natural language for laws about mixtures, because so much of physics cares about how many particles there are, not their weight or volume. Raoult's law, partial pressures of gases, and chemical potentials are all written most cleanly in mole fractions, and unlike molarity, a mole fraction never changes with temperature.
Mix 1 mole of alcohol with 3 moles of water and the alcohol's mole fraction is 1 / (1 + 3) = 0.25, while water's is 0.75 — together they sum to 1.
Mole fraction = a component's share of the total particle count; all shares sum to 1.
The closely related mole percent is just the mole fraction times 100. For gases, the mole fraction also equals the volume fraction and (by Dalton's law) the share of total pressure — handy facts that come from treating gas particles as interchangeable.