What is difference between fit, transform and fit_transform in python when using sklearn?

The confusing part is fit and transform.

 #here fit method will calculate the required parameters (In this case mean)
 #and store it in the impute object
 imputer = imputer.fit(X[:, 1:3])
 X[:, 1:3]=imputer.transform(X[:, 1:3]) 
 #imputer.transform will actually do the work of replacement of nan with mean.
 #This can be done in one step using fit_transform

Your comments tell you the difference. It is saying that if you don't use imputer.fit, you can't do the replacement of nan with some method, for example with mean or median. To apply this process, you need to use imputer.transform after imputer.fit and then, you will have a new dataset without nan values.

See as far as I have understood import a specific class from the library

from sklearn.preprocessing import Imputer

Creating an object of the class which handles the data according to our personalized data

imputer = Imputer(missing_values='NaN', strategy='mean',axis=0)

Applying (as in applying a function on a data) to the matrix x

For example let an operator e applied to data d Imputer.fit returns ed imputer = imputer.fit(X[:, 1:3])

Now Imputer.transform computes the value of ed and assigns it to the given matrice

X[:, 1:3]=imputer.transform(X[:, 1:3])