"Probability of measurable precipitation 40 percent" means 40% chance of rain..
From NOAA: It is "the likelihood, expressed as a percent, of a measurable precipitation event (1/100th of an inch) at a grid point during the indicated valid period." Rain doesn't always hit the ground or fall in a measurable amount. For instance, it can be in the form of virga.

There is a great description of how to read the NOAA forecasts at:
http://pajk.arh.noaa.gov/wxterms.php

http://www.weather.gov/forecasts/gra...csouthwest.php