differences between client-side and server-side data validations in web pages?

Answer 1

As the names imply, client-side happens on the client and server-side happens on the server.

Answer 2

Client side happens at the client level which means that it happens on the browser. This is fast and quick and could be used by implementing some javascript or vbscript code.
The server side happens at the server, it takes longer time and it's rather an old trend unless for security reasons the script should take place on the server.