Preparation 

import pandas as pd
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler

myDataFrame = pd.read_csv("../../scikit-learn-mooc/datasets/penguins_classification.csv")

The set 

target_column = 'Species'
target = myDataFrame[target_column]
target.value_counts()

Adelie       151
Gentoo       123
Chinstrap     68
Name: Species, dtype: int64
target.value_counts(normalize=True)

Adelie       0.441520
Gentoo       0.359649
Chinstrap    0.198830
Name: Species, dtype: float64

Continuation of preparation 

data = myDataFrame.drop(columns=target_column)
data.columns

Index(['Culmen Length (mm)', 'Culmen Depth (mm)'], dtype='object')
numerical_columns = ['Culmen Length (mm)', 'Culmen Depth (mm)']
data_numeric = data[numerical_columns]

data_train, data_test, target_train, target_test = train_test_split(
    data_numeric, 
    target, 
    #random_state=42, 
    test_size=0.25)

data_train.describe()
Culmen Length (mm) Culmen Depth (mm)
count 256.000000 256.000000
mean 43.830469 17.151953
std 5.461854 1.917841
min 32.100000 13.100000
25% 39.200000 15.675000
50% 43.700000 17.300000
75% 48.500000 18.600000
max 59.600000 21.500000 
_ = data_train.hist(figsize=(10, 5))

Normalization 

scaler = StandardScaler()
data_train_scaled = scaler.fit_transform(data_train)
data_train_scaled = pd.DataFrame(data_train_scaled,
                                 columns=data_train.columns)
data_train_scaled.describe()
Culmen Length (mm) Culmen Depth (mm)
count 2.560000e+02 2.560000e+02
mean -2.151057e-16 7.910339e-16
std 1.001959e+00 1.001959e+00
min -2.151915e+00 -2.116907e+00
25% -8.494440e-01 -7.716210e-01
50% -2.393405e-02 7.734577e-02
75% 8.566099e-01 7.565192e-01
max 2.892868e+00 2.271598e+00 
_ = data_train_scaled.hist(figsize=(10, 5))

Conclusion

This transformer shifts and scales each feature individually so that they all have a 0-mean and a unit standard deviation.