When people you're not connected with search for you -- either on LinkedIn or via a search engine -- they see your public LinkedIn profile. Your public profile can include the same information as what your connections see, or you can choose which sections are visible and which aren't.
To find this option, navigate to your Privacy and Settings page. Under the "Helpful Links" subhead within the Profile tab, select "Edit your public profile." The following page lets you either make your public profile visible to no one -- which is not recommended if you're looking for a job -- or visible to everyone.
If you choose the latter, which is the default, you can customize the information that is public. This includes your headline, summary, past positions, honors and awards, groups, education, skills and more. If you're in the market for a new job, you may prefer to keep some of this information private. By default, your name, industry, location and number of recommendations are public.