When you call someone a `wimp', you mean that he is a very weak and timid individual; he is spineless. Other words that have more or less the same meaning are drip and wusses.

 
Example:
Don't be such a wimp, Raju. Just go ahead and take the plunge.
How can you ask someone wimpy like Karthick to be the next President? 

The expression `wimp out' is being used nowadays in informal contexts to mean the same thing as `chicken out'. When you `wimp out' of doing something, you get out of doing it because you are very scared.

 
Exampl:
Sagar said that he would go bungee jumping with me. At the last minute, he wimped out.
If you're serious about doing it, let me know. I don't want you to wimp out.

According to some scholars, the word `wimpy' comes from the word `whimper'. Others believe that it comes from the name of a character in a well-known cartoon show, `Popeye'. J. Wellington Wimpy, affectionately called `Wimpy', is Popeye’s friend. Unlike the star of the show, there's nothing heroic about this roly-poly character. Wimpy is spineless; he never participates in any of the fights that Popeye is constantly getting himself into. The only thing Wimpy enjoys doing is eating hamburgers! "I'd gladly pay you tomorrow for a hamburger today" is his favorite line