loop_and_check.py

phrases = ['Cats are nice', 'Dogs are awesome', 'Python is the best', 'I like doughnuts']
words_to_check = ['are', 'awesome', 'brilliant', 'cake']

# This might be your question
print 50 * "="
print 'Checking pairwise'
print 50 * '-'
for pair in zip(phrases, words_to_check):  # You don't know the zip command yet I think but look it up and this could easily be done using other tools (iterating over things)
    if pair[1] in pair[0]:
        print "Yay, '%s' is in '%s'" % (pair[1], pair[0])
    else:
        print "Oh bother, '%s' is not in '%s'" % (pair[1], pair[0])

print 50 * "="
print 'Checking all words in all phrases'
print 50 * '-'
# This might also be your question
for phrase in phrases:
    for word in words_to_check:
        if word in phrase:
            print "Yay, '%s' is in '%s'" % (word, phrase)
        else:
            print "Oh bother, '%s' is not in '%s'" % (word, phrase)