Google custom search is where you can add a custom search box to your web site or blog. You can set it up to search only your website (internally), or the Internet (externally). The great thing about it is it allows you to show the results on your website through an iframe. This way your visitor never has to leave your website to see the Google search results, however when they "click" on the results of course they'll have to leave your site if your custom search box is set-up to search the Internet (external) instead of just your web site.
An example can be located at a free t-shirt site. You'll see how in this case the search box is in the upper right and the search results show up in the iframe below the search box. Because this particular custom search box searches the internet, when a visitor clicks on an associated "T-Shirt" link they'll end up leaving the site.
To implement it, got to Google Custom Search and choose the topmost link called "Sign up for the basics - it's free" and you're all set!
I hope this helps.