Measurement
Measurement is comparing a quantity to a standard unit with an instrument, producing a number, a unit, and an uncertainty.
Definition
Measurement is using a tool to find out how much of something there is, producing a number and a unit such as $12\ \text{cm}$ or $35\ \text{g}$. It is the process of comparing a physical quantity to a standard unit with an instrument, limited by the instrument's resolution (the smallest division it shows) and read to that resolution plus one estimated digit. A measurement is complete only when it includes the value, the unit, and the uncertainty, which arises from resolution, calibration, environmental conditions, and the operator, and which propagates through every calculation that uses the value. Traceability to SI standards is what makes measurements from different labs comparable.
Example
To measure a bean plant, hold a ruler straight up from the soil and read where the top leaf reaches: $8.5\ \text{cm}$. A millimeter ruler lets you read $84\ \text{mm}$ and estimate $84.5\ \text{mm}$, and a cylinder marked every $1\ \text{mL}$ lets you read $23\ \text{mL}$ and estimate $23.4\ \text{mL}$ at the bottom of the meniscus. A rock's mass of $13.50 \pm 0.01\ \text{g}$ and displaced volume of $5.0 \pm 0.1\ \text{mL}$ give a density of $2.70\ \text{g/cm}^3$ whose uncertainty is about $2\%$, or $\pm 0.05\ \text{g/cm}^3$, dominated by the volume reading, so it is reported as $2.7\ \text{g/cm}^3$.
Key Insight
A measurement always needs a unit; "the plant is 8" could mean centimeters, inches, or leaves. A measurement is a fact about the object plus the tool, not the object alone, and changing the tool changes the number slightly. The weakest measurement controls the uncertainty of the whole result, so effort spent on a better balance is wasted if the volume is read from a coarse cylinder.