Whois is a service that identifies the particular person that owns a domain name (website).
ICANN is a service that protects people's personal information regarding the domain names that they own if they want to opt out.
It completely depends on your needs, but there is some research to suggest that you should keep your Whois information public to allow search engines to identify the true owner that correlates with the business. More of a 'we have nothing to hide' approach.
Take a look at some more of our free SEO tools that are available.