It can sometimes be useful to transform data to overcome the violation of an assumption required for the statistical analysis we want to make. Typical transformations take a random variable and transform it into log x or 1/x or x2 or , etc.
There is some controversy regarding the desirability of performing such transformations since often they cause more problems than they solve. Sometimes a transformation can be considered simply as another way of looking at the data. For example, sound volume is often given in decibels, which is essentially a log transformation; time to complete a task is often expressed as speed, which is essentially a reciprocal transformation; area of a circular plot of land can be expressed as the radius, which is essentially a square root transformation.
In any case, we will see some examples in the rest of this website where transformations are desirable. One thing that is very important is that transformations be applied uniformly. E.g. when comparing three groups of data, it would not be appropriate to apply a log transformation to one group but not to the other two.
Also transformations should only be used to achieve the assumptions of a test. You shouldn’t try lots of transformations in order to find one that achieves a specific test result.