while True means loop forever. The while statement takes an expression and executes the loop body while the expression evaluates to (boolean) "true". True always evaluates to boolean "true" and thus executes the loop body indefinitely. It's an idiom that you'll just get used to eventually! Most languages you're likely to encounter have equivalent idioms.

Note that most languages usually have some mechanism for breaking out of the loop early. In the case of Python it's the break statement in the cmd == 'e' case of the sample in your question.

If you're determined to use a while loop for some reason, it'd be something like this:

i = 0

while True:

    i += 1
    word = words[i]

    if (syllables in word):
        print('Syllables are in word')
    else:
        print('Syllables not in word')

    if i > len(words):
        break

However, this is probably a much worse way to do solve the issue. When iterating through a set it's often more efficient to use a for loop to prevent needless checking of whether the entire set has been checked. A for loop implementation might look like this:

for s in syllable_set_1:
    if s in word:
        print('Syllable ' + s + ' is in word')
    else:
        print('Syllable ' + s + ' is not in word')