If we encrypt the same piece of text using the monoalphabetic substitution cipher and the Vigenère Cipher, we can see why the latter cipher is so much stronger than the former. Let us use a short text about Vigenère to see the difference. Firstly, you can see that the frequency distribution of letters in this messages is fairly typical, with E being the most common letter.

Now, if you encrypt this message using a monoalphabetic substitution cipher, you can see how the frequency distribution changes.

The high frequencies have merely moved to different letters (e.g., the highest peak has moved from E to D, because E has been encrypted as D), and they can be used to crack the cipher. Now, click to encrypt the text using the Vigenère cipher (Keyword CHARLESV) and you will see why it is a better cipher.

As you can see, the frequency distribution is now much flatter. The peaks are less obvious, because each letter has been encrypted in 8 different ways, because the keyword is 8 letters long. The peak that was at E has been shared among 8 other letters. A flatter frequency distriibution means a much stronger cipher.