Measurement is the act of comparing something, X – an object, an event, a phenomenon, anything that can be compared – with an independent standard unit and its multiples, and then assigning the corresponding quantity of units to X as the measure of that aspect (characteristic, property) of X.
I want to focus on the independence of the measurement standard. This is easy to see in the case of clocks. Every clock is independent of events that happen at points of time measured by the clocks. But so is every ruler or measuring wheel independent of the objects they measure.
In order to measure movement we need measurements with the same standard at two or more points. To measure rates of movement requires (1) measurements with the same standard at two points in time or space along with (2) measurements of a different property at the same two points in time or space. The first two measurements (1) are chosen independently of the second two measurements (2). The second two measurements (2) use an independent standard of measurement but are measured at the times or places corresponding to the first two measurements (1); that is, the second two measurements (2) are dependent on the first two measurements.
Measurement is only possible because of the homogeneity and isotropy of space and time. Because of that, measuring devices can be moved to an object, event, phenomenon, etc. in order to measure it by contact in space and time. Or signals may be used to measure non-contact objects and non-simultaneous events, but relativistic considerations will apply.