Reduced, in cooking, means boiled down until thicker and stronger. A reduced sauce, reduced by half, reduce the liquid.
Simmering drives off water and concentrates what is left, so a reduced sauce is more intensely flavoured as well as thicker. Reduce by half is the standard instruction. Outside the kitchen, reduced means made smaller in any sense — reduced prices, reduced staff, reduced circumstances, which is a delicate old phrase for having lost money. Note reduced to, meaning brought to a worse state.
Practised in Smell & Taste