Building dataframe with label count

If need indicator columns (only 0 or 1):

Use MultiLabelBinarizer:

from sklearn.preprocessing import MultiLabelBinarizer

mlb = MultiLabelBinarizer()
df1 = pd.DataFrame(mlb.fit_transform(df['target']),columns=mlb.classes_)
print (df1)
   Aging  Brain  Dementia  Genetics  Neurons
0      1      1         0         1        1
1      0      0         1         1        0
2      0      1         1         1        0

Or Series.str.join with Series.str.get_dummies - but it is slowier:

df1 = df['target'].str.join('|').str.get_dummies()

If need count values in lists:

data = [{'target': ['Neurons','Brain', 'Neurons', 'Neurons']}, 
        {'target': ['Dementia', 'Genetics']}, 
        {'target': ['Brain','Brain', 'Genetics']}]

df = pd.DataFrame(data)

from collections import Counter
df = pd.DataFrame([Counter(x) for x in df['target']]).fillna(0).astype(int)
print (df)

   Brain  Dementia  Genetics  Neurons
0      1         0         0        3
1      0         1         1        0
2      2         0         1        0

Maybe this will help

# Instead of creation of target list ,
# Convert list of str to one single str 
list_to_str = [" ".join(tags['target']) for tags in data]

##
#['Aging Brain Neurons Genetics',
# 'Dementia Genetics',
# 'Brain Dementia Genetics',
# 'Neurons Brain Neurons Neurons'
# ]

# Using CountVector
from sklearn.feature_extraction.text import CountVectorizer
text_data = np.array(list_to_str)

# Create the bag of words feature matrix
count = CountVectorizer()
bag_of_words = count.fit_transform(text_data)   # needs to coverted to array

# Get feature names
feature_names = count.get_feature_names()

# Create df
df1  = pd.DataFrame(bag_of_words.toarray(), columns=feature_names)

print(df1)

## Output
   aging  brain  dementia  genetics  neurons
0      1      1         0         1        1
1      0      0         1         1        0
2      0      1         1         1        0
3      0      1         0         0        3