How do decision tree works for feature selection?

Question

I have a dataframe with a feature selection problem. I want to get the variables explaining the variance within each segment of the following dataset:

    Do you agree    Gender  Age     ...  City          Urban/Rural  Output
0   Yes             Female  25-34   ...  Madrid        Urban        Will buy
1   No              Male    18-25   ...  Fès-Meknès  Rural        Won't
2   ...             ...     ...     ...  ...      ...               Undecided
....

The target being Output.

I've been told a decision tree could be a way so after googling a bit I did:

# Feature Importance with Extra Trees Classifier
from sklearn.ensemble import ExtraTreesClassifier

# feature extraction
model = ExtraTreesClassifier(n_estimators=10)
model.fit(X, y)
print(model.feature_importances_)

Which returns:

[0.         0.00473011 0.00716472 0.00778101 0.0051573  0.00139121
 0.02045262 0.00791912 0.         0.00222593 0.00173901 0.00417362
 0.00222593 0.00313295 0.00565095 0.00652543 0.         0.00527774
 0.         0.         0.00601354 0.         0.         0. ...

This looks exactly what I am looking for, but I don't get how we obtained this output. It look a bit like a black box. I am eager to learn and to do it myself to understand.Can you explain to me or refer me some resoures that would help me implement it myself?

Annex: data preparation

def load_dataset():
    connection = psycopg2.connect(user = "user",
                                  password = "password",
                                  host = "host",
                                  port = "5432",
                                  database = "database")
    connection.set_client_encoding('UTF8')
#     connection.set_client_encoding('UNICODE')
    sql = "select * from capi limit 10;"
    # load the table
    df = pd.read_sql_query(sql, connection)
    # retrieve numpy array
    dataset = df.values

    # split into input (X) and output (y) variables
    filtered_cols = ['Output']
    cols = [col for col in cols if col not in filtered_cols]

    X = df.loc[:, cols]  #independent columns
    X = X.astype(str)
    y = df['Output']    #target column i.e price range
    return X.values, y.values

X,y = load_dataset()