While in Caesar cipher, each letter of the plaintext is shifted by same number; in vigenere cipher, each letter is shifted differently, based on letters of the key.
Suppose this is your plaintext: Attack at dawn
and a 'key' word is: apple.
Then, the letters in the plaintext can be encrypted by shifting each of them with a corresponding letter in the 'key'; like the following:
Plaintext: A,t,t,a,c,k a,t d,a,w,n
Keyword: a,p,p,l,e,a p,p l,e,a,p
Shift by: 0,15,15,11,4,0 15,15 11,4,0,15
Cipher: A i i l g k p i o e w c (this is the ciphertext).
That is it.
Since, each letter is being shifted differently, this cipher is a simple form of Polyalphabetic substitution.
About the name 'Vigenere', it's quite strange and a historical 'mistake', as Mr. Vigenere has nothing to do with this cipher technique. The technique has been invented and reinvented many times in the past.
According to the Wikipedia, " The method was originally described by Giovan Battista Bellaso in his 1553 book La cifra del. Sig. Giovan Battista Bellaso; however, the scheme was later (in 19th century) misattributed to Blaise de Vigenère in the 19th century, and is now widely known as the "Vigenère cipher". In reality, Blaise de Vigenere presented a similar but stronger cipher before the court of Henry III of France, in 1586. But noone remembers him for that! History is mystery. sometimes. Anyway.
A curious comment on this technique might interest you.
In 19th Century, the vigenere cipher gained a reputation for being exceptionally strong. It was even called 'unbreakable' by the noted author and mathematician Charles Lutwidge Dodgson in his 1868 piece "The Alphabet Cipher" in a children's magazine. Who was he? You may know him by the name Lewis Carroll, the author of the famous "Alice's Adventures in Wonderland"!
In this technique (vigenere cipher), we were using a keyword's letters to 'shift' each of the plaintext's letter.
If we try to see the big picture, this and the previous techniques like caesar cipher and the one time pad, all use a process of 'substitution', to take a plaintext and a key, and give us a 'ciphertext', which looks gibberish at first sight; but can be decrypted if the 'key' is known.
One other way to achieve this 'encryption' effect, is to literally 'scramble' or 'change-the-positions-of' the letters in the plaintext. Such a scheme will be called a 'transposition' cipher, and will be discussed soon.
But, before that, we will look at some of the other classical techniques of encryption - one of which has, even gave us one of the most popular unsolved and unbroken code of all time. See you soon, with a story and a technique called - Book Cipher.
Bye till then.