Linkedin is a huge, online database of professional profiles. Anyone can create a professional profile. Then, you start sending invitations to other people to connect to you. But what does connecting mean?
Essentially, it means that I can see your information and you can see mine.
Let's say that I send an invitation to Bill Smith and he accepts my invitation. That means he's my first degree contact. First degree means that he's one person away from me.
Me --> Bill Smith (1 degree away from me = 1st level connection)
Bill is connected to Suzy Frick. She's not connected to me directly but she is connected to Bill. She is his first degree contact and that automatically makes her my 2nd degree connection - which means that she is two people away from me.
Me --> Bill (1 degree) ---> Suzy (2 degrees)
Now, Suzy is connected to Blanche Jones. Blanche is not connected to me directly. She is, therefore, my 3rd degree contact. That means that she is three people away from me.
Me --> Bill (1 degree) --> Suzy (2) --> Blanche (3)
Why are degrees important?
In the old days, when you did a search on Linkedin, it would only return people who were 1, 2 or 3 degrees away from you. That meant that you had to connect to as many people as possible to be able to search a large pool of people. You also had to be connected to as many people as possible to make yourself find-able by a large number of people.
That's gone by the wayside. Now, you don't need to be connected to anyone to be found in a search. But Linkedin added a new twist. When you do a search on Linkedin you can only see the full names of people who are your 1st and 2nd degree connections. If someone is a 3rd degree connection you can only see the first name and the first initial of the last name. If someone is beyond three degrees you can't see the name at all. So it still pays to be connected.
There is an exception to this rule. You can see the full names of the people who are in the same Linkedin groups as you are. So, it makes sense to join the relevant groups.