Measurement
Measurement is the act of quantifying a property of an object or relation. Quantification requires there exist a standard unit; measurements are expressed as multiples of the standard unit (or as a ratio of the dimension measured to the dimension of the standard unit). A count is distinct from a measurement, in that a count quantifies the number of distinct objects, and can thus be exact, while a measurement is never entirely exact.
Units of measurement
Historically, there have existed a wide variety of standard units; most measurement for scientific and commercial purposes today uses the standard units of the International System of Units (abbreviated SI from its name in French, Système international d'unités). However, in the United States of America, much measurement is performed using United States customary units instead.
Accuracy and precision
Accuracy is the measure of correctness of a measurement; precision is the measure of the repeatability of a measurement. Systematic errors in the measuring equipment or technique can cause measurements to be inaccurate - to produce a result which is incorrect, and repeatably so. (A simple example would be using a ruler which was not properly calibrated.) Random errors in measuring equipment or technique will cause a lack of precision in a measurement; a measurement is considered more precise when the deviations between repeated measurements of the same quantity are lower.