What's the difference between fit and fit_transform in scikit-learn models?
To center the data (make it have zero mean and unit standard error), you subtract the mean and then divide the result by the standard deviation:

$$x' = \frac{x-\mu}{\sigma}$$

You do that on the training set of data. But then you have to apply the same transformation to your testing set (e.g. in cross-validation), or to newly obtained examples before forecast. But you have to use the exact same two parameters $\mu$ and $\sigma$ (values) that you used for centering the training set.

Hence, every sklearn's transform's fit() just calculates the parameters (e.g. $\mu$ and $\sigma$ in case of StandardScaler) and saves them as an internal object's state. Afterwards, you can call its transform() method to apply the transformation to any particular set of examples.

fit_transform() joins these two steps and is used for the initial fitting of parameters on the training set $x$, while also returning the transformed $x'$. Internally, the transformer object just calls first fit() and then transform() on the same data.