While there are free profiles that allow you to interact normally in the site, LinkedIn memberships offers you extra features on payment.
One such difference is messaging. While a free user can only message those people he knows in the site, you can use InMail to message people outside of your direct network. Memberships offer you a certain amount of InMails per month.
You can also use the Profile Organizer premium feature to sort out your profiles into folders, add details of your own, and even track the changes they make. This is especially useful for recruiters keeping an eye on possible employers.
Basic membership also caps the amounts of profiles you can view each month. Paid memberships do not limit that.
Yet another difference is knowing who saw your profile. Upgraded membership gets extra information on who saw your profile and statistics about what searches you appear on and for what keywords.