I saw lot of questions about vanity addresses, but not sure what is vanity address. Could someone please explain?
It is the same thing as a vanity plate which are used for cars. That is: An address which you choose yourself (or at least part of it). For example the address of Bitcoin24 is 1BTC24yVKQdQNAa4vX71xLUC5A8Za7Rr71 (watch the first six characters!).
See this question How can I generate a vanity Bitcoin address?