The .apply() method in Pandas is used to apply a function to each row or column of a DataFrame. It is a very versatile method that allows you to perform complex operations on your data with just a few lines of code.

The basic syntax of the .apply() method is as follows:

df.apply(func, axis=0, args=(), **kwargs)

Here, func is the function you want to apply, axis specifies whether you want to apply the function row-wise (axis=0) or column-wise (axis=1), args is a tuple of additional arguments to pass to the function, and **kwargs are any additional keyword arguments to pass to the function.

For example, let's say we have a DataFrame of student grades:

import pandas as pd
 
grades = pd.DataFrame({'name': ['Alice', 'Bob', 'Charlie'],
                       'math': [80, 90, 70],
                       'science': [75, 85, 80],
                       'english': [90, 85, 75]})

We can use the .apply() method to calculate the average grade for each student:

def average(row):
    return row.mean()
 
grades['average'] = grades.apply(average, axis=1)
 
print(grades)

Output:

      name  math  science  english  average
0    Alice    80       75       90     81.67
1      Bob    90       85       85     86.67
2  Charlie    70       80       75     75.00

In this example, we define a function average() that takes a row of the DataFrame as input and returns the mean of the row. We then use the .apply() method to apply this function to each row of the DataFrame using axis=1. The resulting averages are added to a new column called 'average' in the original DataFrame.