Client-side code is code in a client-server system (most often the web) that is executed on the client machine - for instance, most javascript code is client-side.
Compare with ServerSide.
The advantages of Client-side code are that you get faster response times than by using server-side code and can do things that can't be done with server-side code.
The main disadvantage is that you can never be quite sure what the client your code runs on will support. This means many fancy web pages will break in an unexpected web browser.