Vocabulary: do we measure actual values or observations? Consider that $\theta$ is an hidden parameter and one has an observation such that $O$:
$$
O \sim N(\theta,\sigma^2).
$$
My question concerning vocabulary: 
do we measure $\theta$ and it gives us $O$? (so we measure the true value)
or 
do we measure $O$ ? (so we measure the observation)
I am looking for unquestionable sources.
 A: Statistics doesn't give a special meaning to 'measurement' in the way it does to 'estimate'. (As @Glen said, we 'estimate parameters'.) So it's going to depend on your area of application and on what $O$ and $\theta$ represent.
If the variance $\sigma^2$ describes the measurement error of some instrument or procedure, and $\theta$ is some property considered rather inherent to the thing being measured, it's natural to talk about 'measuring $\theta$', and about the $O$s as 'measurements of $\theta$'. E.g. the $O$s are several measurements of the length $\theta$ of a steel shaft.
If the variance $\sigma^2$ describes the variability of different individuals, and $\theta$ is some feature of the population considered rather contingent, it's not so natural to talk about 'measuring $\theta$'. E.g. the $O$s are single measurements of the lengths of each steel shaft from a batch, rather than measurements of the average length $\theta$ of a shaft in the batch .
In any case 'measuring an observation' is oddly worded; 'making an observation' is usual. 
