What does it mean to measure something? And does the definition of measurement work well for length, area, weight, volume and time?

Since this is not my area of expertise, I searched Google under the key words "measurement" to get these possible sources:

http://www.aaamath.com/mea.html
http://en.wikipedia.org/wiki/Measurement
http://oncampus.richmond.edu/academics/education/projects/webunits/measurement/
http://www.socialresearchmethods.net/kb/measure.php
http://www.unc.edu/~rowlett/units/

In the future, you can find the information you desire more quickly, if you use appropriate key words to do your own search.

I hope this helps. Thanks for asking.