By default, when BigHits4U.COM sends traffic to your website, the target website will see that the visits are coming from

The Traffic Source feature enables you to change what the target website sees as the traffic source / referrer for the visits coming from

When you choose the Anonymous source for your website, there will be absolutely no information about the origin of the hits. It will be as if the visitors typed in the address of the promoted website directly into their browser. Google Analytics will show such hits as Direct hits.

You can also choose to use a custom URL as the referring website. This way, you can make it look like the traffic is coming from for example.