Why is it necessary to correct the pressure of a gas that is collected over water?
Generally, gases which are insoluble in water are collected by putting them into an inverted vessel via a tube, so that the gas rises to the top and 'displaces' the water downward. Take a look at the following picture—



Now, the problem is that water has a certain vapour pressure at any temperature. In other words, whenever water is exposed to a gaseous phase, it will start to evaporate until the partial pressure of the water vapour in the gas phase reaches a certain value (this value depends on the temperature). This value is known as the 'vapou pressure of water'.

In this case, the gas you collected by displacing the water will be contaminated by water vapour. Therefore, the pressure of the gas which you measure will be the sum of the partial pressure of the product gas, and partial pressure of water vapour.
$$\begin{align*}
Measured\;pressure &amp;= Partial\;pressure\;of\;product\;+\;partial\;pressure\;of\;water\;vapour \\
&amp;=Actual\;pressure + Vapour\;Pressure
\end{align*}$$ This means that you must correct the pressure, by subtracting the vapour pressure of water from the measured value to get the actual pressure of the produced gas.

Note: There are standard tables which list the value of vapour pressure of water at different temperatures. These tables are generally used for the correction.