There are many sites (including apps) which request access to your contacts.
I would assume that you answered yes to this type of question. You would also have given them access to your email password in order for them to access your contacts. I will admit that it is deceiving and it could look like you were singing into the site, when what you are really doing is providing your email password (but this would only hold true if your email password and your linked in password were the same)
What also happens on Liinked In - is that based on your profile (where you live, and the type of industry/companies you worked in) - Linked in makes recommendations for people that you may want to connect with.
For example, If I worked for CocaCola - and if I went to the section where Linked in Makes such types of recommendations - it would show me profile pictures of other people who work for CocoCola based on our joint network. If I worked in Production for CocaCola - it might recommend that I also connect with people who work in Production for Pepsicola, Kraft, General Mills etc.
As a result of those recommendations, people may see you as someone that linked in thinks they should connect with, and they will/could send you a request.
Many people use Linked in as a marketing or networking tool. Personally, I just use to keep in touch with business colleagues and watch people jump from company to company. It's kind of like facebook for business people.